Short Answer:

Yes, certain classes of soporifics/sedatives/hypnotics do alter circadian SCN gene expression

Long Answer:

It's been shown that some (though not all) non-melatonin based hypnotics can improve the symptoms of jet lag disorder and promote nocturnal sleep (PMC3020104). The American Academy of Sleep Medicine did a very useful review and grading of the evidence for intrinsic circadian rhythm sleep-wake disorder treatments that you should look at (PMC4582061).

The question really is more about whether the mechanism of action of these drugs is direct or indirect (i.e. do they primarily interact with SCN gene transcription factors/regulatory pathways, or are the changes wholly secondary to sleep induction and altered light exposure)?

The answer is likely some complex interaction of the two, but the best evidence is in support of an the interaction between GABA and SCN function being responsible. 

Most classes of non-melatonin based hypnotic drugs (benzodiazepines, quinazolinones, barbituates, etc...) will positively enhance GABA signalling in the brain to elicit a sedative state. It's been shown in vitro/ex vivo that GABA signalling inhibits neuronal activity in the SCN and is important for clock neurons' synchrony (PMID10707977, PMC1748197, PMC3683151, PMID12750413). In vivo use of anxiolytics (with sedative properties) have been shown to modulate Per1/2 gene expression in animal models (PMC1571793, PMC1572494). Additionally specific GABA A receptor agonists have been shown to alter period mRNA levels in the SCN of rodent models (PMID17156208, PMID18258754).

If you're looking to tip your toe into circadian stuff I'd recommend getting your hands on a copy of Russell Foster & Steven Lockley's book 'Sleep: A Very Short Introduction'. It's not much bigger than an iPhone 6 plus and just over 100 pages, so you'll blast through it, but it's brilliant for getting a primer in the field! It certainly helped me get to grips with some of the issues when circadian physiology started infiltrating my own field in the last few years!  

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3020104/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4582061/

https://www.ncbi.nlm.nih.gov/pubmed/10707977

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1748197/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3683151/

https://www.ncbi.nlm.nih.gov/pubmed/12750413

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1571793/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1572494/

https://www.ncbi.nlm.nih.gov/pubmed/17156208

https://www.ncbi.nlm.nih.gov/pubmed/18258754

Thanks Keith!

I anticipated the answer would be some do, some do not, and others we have no idea about. The first two papers look very useful! We might have to reconsider the term "sleeping-pills" as "pills that modify the temporal organisation of physiology" in some cases.

And I appreciate the effort you put in to the answer!

I would redefine sopofiric, since it tends to be associated to GABAA positive allosteric modulators, but there is a plethora of drugs that can affect SCN gene expression. First there are the GABAB agonists, mainly GHB and Phenibut (Of which I've noticed an increased abuse), opioids, SRIs, which is relevant since some tricyclics, trazadone and similar antidepressants are prescribed off label for sleep. I'm particularly curious in anticholinergic drugs disrupting it since we take so many of them, and some even specifically to sleep (doxylamine, dyphenidramine).

Thanks Tomás!