Is it possible to have blood group A plus and genotype AA

First of all, I assume you mean A-positive (as opposed to A-negative), not A-plus.
Secondly, the genotype AA refers only to the A part, and not to the "positive".
The 2 are completely independent of each other.
Third, the so-called ABO genotype of someone with type A blood (positive or negative) may be either AA or AO. So the answer to your question is "yes".