I haven't gotten to play SRMS4, but I did read them all over. I was going to do this as a way to get my players used to SR5. We ended up just running SRMS5 in the end though.
I've looked over the SRMS4 modules and from what I can see, there's no REAL reason not to do it for a private group. The only caveat is that the NPCs in SRMS4 tend to be ever so slightly lower powered than their counterparts in SRMS5 (example, in 4 the dicepool for Gymnastics for a Big Bad might be 10, in 5 it's 12). That's just the nature of going from 1-6 skill ratings to 1-12.
Really though, everything else is pretty easy to convert over. Armor 7-9? then it's an 8. No accuracy or limits? work it out. The stats on the creatures and NPCs are all the same (Body-Charisma+Mag/Resonance). You'll just have to futz with the weapons/commlinks a bit. If there's a decking run (rare) then you'll need to use your own judgement on how to configure the Spider's deck and programs (as they're WAY different).
Overall though? Yeah, go for it.