It should work, though you'll have to screen multiple clones to make sure the insert is in the desired orientation. If the vector is only digested by one enzyme, then the insert can be ligated into the vector in either the forward or reverse compliment orientation. This is in contrast to the typical restriction enzyme cloning method which uses two enzymes that produce different sticky ends, which (hypothetically) guarantees that all clones with the desired insert will be in a single orientation.
Definitely dephosphorylate the digested vector extensively before ligation to ensure it can't ligate back together without the insert. Otherwise most clones you screen will contain the original plasmid.
In addition to what Alexandra Johnson said, design a diagnostic digest test with a site unique to your insert to screen through your colonies. Also, ensure your FastAP used for dephosphorylation has not undergone too many freeze-thaw procedures.
Good luck!
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