Does reversion of resistant strains to wild-type only occur when no more drug pressure is exerted
I am not an expert on HIV but I am answering based on general principles.

This is a typical example of selection of individuals/populations with different fitness.

Reversion to wild-type (WT) would happen if the WT has higher fitness in that environment. Assuming that WT is the fittest under drug-free conditions, it is not difficult to understand that the WT population will outgrow other mutants. 

For your question — "would a drug resistant HIV population revert to WT under treatment with other drugs", the simple answer would be no.



Explanation

HIV generally acquires resistance against different drugs quickly because it has a high mutation rate. In your example case, the HIV population that is resistant to the new drug will outgrow other populations if we assume that the selection is strong. There would not be any reversal to WT because WT would also be unfit in the new environment. If the selection is weak then the population genetic diversity would depend on the relative fitness of different genotypes. 

There may also be pleiotropic effects: mutations that provide resistance against one drug can also possibly provide resistance against other drugs. This is well known in case of bacteria and there are many reports for HIV too (Rhee et al, 2010, Other Google Scholar Hits).