There is no existing function for this purpose. Manually calculating it is easy: Using Multiwfn to simulate spectrum, export the two curves as text files,  import them into e.g. Origin, define a new column as their overlap, then perform numerical integration.

Dear Professor Tian-Lu
Is it possible to compute overlap integral between two spectra? I ask about in context of computing Dexter Energy Transfer rate.  Maybe Multiwfn has option to do it as well?
Cheers.