So, all in all, the rule of thumb seems to be: EQing MIRx-ed instruments works universally fine, while compressing them will yield post-verb compression results - which can end up satisfactory, but can also lead to less-than-desired effects, depending on the desired effect and compression amount.
Overall, I'm excited about MIRx - it's just a fantastic product in terms of functionality, ease of use and pricing. But if I was to put one thing on some personal wishlist for further development of MIRx, it would be some form of routing flexibility, just so to be able to do some processing like compression pre-MIRx when the situation calls for it.