Can I tighten unused terminal screws on my outlets?
As far as snuggling the screws down there will be no problem in doing this. I would put the wire under the screw or clamp and a couple of wraps of electrical tape. Back stabs are the #1 failure point in wiring in the US.  I would say failing Back stabs cause over 90% of the wiring failures since you are doing this save yourself some time and use the screw terminals or you may end up like so many others that ask why are 1/2 of outlets in my room not working.