That's an excellent question. Recently, a drug company tried treating MS patients with a compound that blocks all T-cells from entering the central nervous system. In several of the subjects, this removal of immune "surveillance" of the nervous system permitted the rapid replication of a virus that many people have chronically lurking inertly in their CNS; it's called JC (and you thought it was the Holy Ghost that dwelt in you!). Once relieved of immune control, the JC virus actually killed some of the subjects, and the therapy was halted.
We're trying to ALTER the T-cell actions rather than suppress them. Specifically, we are testing a strategy that would only affect the T-cells that are attacking "self" molecules. So, the ones that are attacking viruses or other agents should still work fine.