Q: Can meta-analysis be done to compare the efficacy of one drug against two diseases?
A meta-analysis is a type of literature or systematic review that statistically combines the findings of previous studies on a problem. The aim is to determine the global effectiveness of the remedy or solution. In other words, the aim is to study the effectiveness of treatment X for one disease A.
What you are attempting is to study the effectiveness of X for two diseases, A and B, that is, whether X works better for A or for B. Without having more information on what you have in mind, we are not sure how this would be relevant. (What could be useful perhaps is a multiple treatments meta-analysis, one that studies the effect of, for instance, treatments X, Y, and Z on A.) Another consideration would be the number of existing such studies to be able to do a comprehensive meta-analysis.
However, you could check these aspects for yourself by doing a preliminary literature search. You could also search a systematic review registery, such as PROSPERO, as you would anyway need to register your meta-analysis in such a database before starting with the study. The result of the search will help you decide whether or not this research question would be feasible to pursue.
Hope that helps. For more insights into meta-analyses and systematic reviews in general, you may also go through these resources: