If a prior art inventor did not appreciate an inherent use/function at the time of his invention, can that inherent use/function be patentable if discovered at a later time?

No, because there is no requirement that a person of ordinary skill in the art recognize the inherent disclosure at the time of invention, but only that the subject matter is in fact inherent in the prior art reference. Schering Corp. v. Geneva Pharm. Inc., 339 F.3d 1373, 1377, 67 USPQ2d 1664, 1668 (Fed. Cir. 2003) (rejecting the contention that inherent anticipation requires recognition by a person of ordinary skill in the art before the critical date and allowing expert testimony with respect to post-critical date clinical trials to show inherency).  See MPEP 2112.