Is their WE likely to bottom out if that's the case?

On my Dartmouth team (Iba), I have one SR and two JR PG.  I'd like to use it on the lower overall rated JR to break up the classes more evenly.  The SR has a 100 ST and will try to get 27-28 min/gm from him, so won't be enough minutes for two other points.  I tried that last year and both backups wound up dropping a some WE points over the year due to little PT.

Go ahead and try. You can always remove the redshirt if you don't like the result. And then you can try someone else! And remove THAT one if you want. Work your way through your entire roster if you want. 

Common sense and odds apply here.  Random thoughts on things that affect red-shirting in no order....
How many players at that position? More makes it easier.
How good is player especially related to rest of team? Gooder(?!) player less likely to redshirt.
Age of player? Older less likely.

I've had a JR take a redshirt but it is VERY rare. 

I have had it happen but like cammby said it is rare