Your situation could be more complex than the simple answer I'll give, but here's my answer:
Yes, you can appraise the single parcel. It has its own legal identity (presumably) and can be encumbered/traded/sold/given away (presumably). The tax ID number is something assessors use to track assessments for tax purposes; not used (although there is usually a correlation) for identifying legal parcels.
Since this is for a mortgage loan, I'd probably alert my client to the APN situation and request a copy of the preliminary title report.
I do vacant land but rarely have to deal with odd-ball issues; a lot of other appraisers on this forum regularly deal with odd-ball vacant land issues. So, wait for a few more responses to get the general consensus.
Good luck!