Is this a feasible synthetic route for 1-(phenylethynyl)cyclopentan-1-ol?
The route definitely looks feasible and it is more or less what I would have done to arrive at your desired product. A few notes:


Make sure you actually have sodium amide $\ce{NaNH2}$ and not sodium in ammonia $\ce{Na/NH3}$. As pointed out in the question comments, they react very differently; the latter generates a trans-alkene.
I’m not sure I would have chosen the same base. But the choice of base is likely arbitrary anyway. n-Butyllithium would definitely also do the trick but might be overkill.
Typically in a lab setting, reactions with strong bases (as is the case here) are carefully quenched with something aquaeous. So you can be sure that there will be an aquaeous proton source ($\ce{H2O}$ or $\ce{H+/H2O}$, depending on your markers’ preferences) in the end. There should be no need to additionally specify conditions. It would make no sense to attempt to isolate the alcoholate anyway.