Yes, it would. I would use t-BuOK (pKa = 17) if I want to deprotonate only a primary alcohol (pKa = ca. 15-16) to form an alkoxide in the presence of a secondary amine (pKa = ca. 36).

Compare the acidity of alcoholic O-H to that of secondary N-H Bond.

The question is if tert-Butyloxid is not also reacting with the alkoholic O-H.

So you would need to acetylate the O-H reversible by Acetanhydrid. Then the N-H firms a quarternary aceticacetatsalt. Carefully dissolve the salt in weak hydrogencarbonat to isolate the Amin- ethylacetat without quarternary salt. Then you watch to be absolute waterfree dry. Dissolve it in some absolute ether and put carefully stoichiometric amount of NaHydrid to the well stirred and cooled solution.

The H2 gas wich is formed is leaving the reaction as gas and the Amidic Salt NR2-Na is isolated after carfully rotavapation of the ethersolvent.

Handle NaHydrid very safe, because if there is any trace of water it starts burning very easy.

A good problem-solving algorithm when facing this kind of question is to find a copy of Jerry March's Advanced Organic Chemistry and spend a day looking up the references listed in the footnotes, as well as the listed procedures in Organic Syntheses, which are available in any self-respecting science library. "A week in the lab saves a day in the library" we used to say in grad. school. In the 2007 version of AOC (6th Ed.), reaction 10-8 covers all the foregoing suggestions and then some.

Blocking the amine group by forming a beta-hydroxyamide is fraught with problems due to the propensity for 5-member rings to form; see for example Facile synthesis of the four 3-aminocyclopentane-1,2-diol stereoisomers

Jeffrey P. Whitten, James R. McCarthy, and Michael R. Whalon. J. Org. Chem. 1985, 50, 22, 4399–4402

Publication Date:November 1, 1985

https://doi.org/10.1021/jo00222a045

My favorite way of alkylating a primary alcohol in the presence of a secondary amine is to first treat the amino alcohol with 1.0-1.1 equivalents of a boron-centered Lewis acid like BF3 (even BH3 will work if there are no reducible functional groups). The reaction in THF requires 1-3 hours (follow by TLC) at reflux for stubborn amines (hindered and aryl amines), but is practically instantaneous with the amino alcohol you describe. Evaporation of the reaction (-THF) and reflux in methanol followed again by evaporation removes excess Lewis acid. If you don't treat with base, the alcohol group remains free. Now the boron-complexed amine is non-nucleophilic and can be recrystallized from boiling alcohols. The pure complex can then be treated with 2,6-di-tert-butyl pyridine or a similar, hindered, tertiary amine base (a Hünig's base)(1.01 equiv.) in DMF (aim for a 0.2-0.5 M solution), cooled to any convenient temperature below 0 C (e.g., -20 C), and alkylated with a sufficiently powerful electrophile like methyl mesylate, or an alkyl triflate. After stirring the mixture below 0 C for an hour, the reaction is allowed to warm to ambient and stirred overnight. Monitoring by TLC or NMR of worked-up aliquots tells you when the reaction is done or not progressing. The product is worked up by acidification (1 N HCl aq. to pH 4), washing to remove amine bases as water-soluble hydrochlorides (greasy Hünig's base hydrochlorides frequently dissolve in ether if water is present), followed by neutralization (concentrated NH4OH added dropwise to pH 10), and typical extraction procedures.

I couldn't find a published procedure. Specifically, my favorite way to work this type of reaction up is to evaporate as much DMF as possible in vacuo, suspend the residue in half-saturated sodium chloride in water (mix saturated sodium chloride solution with an equal amount of distilled or DI water), acidify (1N HCl) to break the borate complex, wash out the 2,6-di-tert-butyl pyridine with 3 extractions using a few mL of ether per 10 mL of brine (your amine will be a hydrochloride salt and will stay in the aqueous layer; save the ether layer and test it by NMR to be sure no product is present), render the brine basic with ammonium hydroxide, extract with 1:1 ethyl acetate hexane, 3 or more small portions as with the ether washes, combining of the ethyl acetate/hexane layers, drying (MgSO4 is superior to Na2SO4 when DMF is still present), filtration and evaporation to give crude product as a free amine. Each part of the procedure has an advantage: acidification gives a water-soluble product as amine hydrochloride plus water-soluble borates, concentrated ammonium hydroxide generates water-soluble ammonium chloride and leaves a residual amount of base (ammonia) that can be evaporated easily from the product (compared to sodium or potassium hydroxides or carbonates) in the next step with fewer side reactions, ammonia consumes excess alkylating reagent like triflates, and 1:1 (v:v) ethyl acetate-hexane mixtures partition DMF residues in to the aqueous layer (DMF doesn't tolerate hexane and vice-versa, so it should stay in the aqueous layer), so there should be no DMF in your amine product. These are the tips I've relied upon successfully for decades. Similar procedures can be gleaned from OS recipes, for example, the use of hindered base N,N-diisopropylethylamine (DIPEA):

1. Part B of SYNTHESIS OF ALPHA-HALO ETHERS FROM SYMMETRIC ACETALS AND in situ METHOXYMETHYLATION OF AN ALCOHOL

Martin Berliner and Katherine Belecki. Org. Synth. 2007, 84, 102

DOI: 10.15227/orgsyn.084.0102--shows typical procedure for isolating a pure product after using DIPEA.

2. If alkylating agent used with an un-blocked amine, DIPEA can cause alkylation of it: See part A of TRANSFORMATION OF PRIMARY AMINES TO N-MONOALKYLHYDROXYLAMINES: N-HYDROXY-(S)-1-PHENYLETHYLAMINE OXALATE

Hidetoshi Tokuyama, Takeshi Kuboyama, and Tohru Fukuyama

Org. Synth. 2003, 80, 207

DOI: 10.15227/orgsyn.080.0207

3. The boron-complexing chemistry is unpublished research performed in industry, based on the work of H.C. Brown and David Knapp in their discussions of MIDA-borinates and how they were developed. See for example A General Solution for Unstable Boronic Acids: Slow-Release Cross-Coupling from Air-Stable MIDA Boronates

David M. Knapp, Eric P. Gillis, and Martin D. Burke*

View Author Information

Cite this: J. Am. Chem. Soc. 2009, 131, 20, 6961–6963

Publication Date:April 30, 2009

https://doi.org/10.1021/ja901416p

Best wishes.