TOPIC:

I am considering to get 2 subs which do not have any built-in DSP. I was trying to figure out whether I can use miniDSP for the sub only, without altering the signal chain for the rest of the system. 

Is there any significant downsides of connecting my amp’s sub output to the miniDSP, and connecting miniDSP to the subs? 

It would be helpful to know exactly what equipment is in your system and how you've got it wired now.

If your amp has a dedicated sub output in principle this will work. Unless your amp allows it you won’t be able to apply a filter for where the mains roll off.