Question

Would globally widespread HIV increase the frequency of the resistance allele if anti-HIV drugs were widely available and effective?

Answer 1

In a word: No.

Explanation:

Disease resistant alleles spread through a population because the disease resistant individuals don't die, so reproduce more and spread their alleles.

Introducing effective drugs that stop the infected from dying makes them just as able to have offspring as the resistant, making the only other (natural) way to increase the resistance allele frequency in the population be that the resistant have more children than the non-resistant.