It's in a school's interest to get the restriction removed so they are unlikely to add any further conditions to the process. In fact the minima specified by the CAA are quite sufficient for a fledgling FI(R) to gain the necessary experience and judgement to send people off on their first solos so I don't anticipate any roosting chickens - the process has been in place long enough for that to have happened if it was going to.
The school I was at when my restriction was removed made sure that I had recommended a few people for first solo, which a suitably qualified FI then approved, as part of my 'runup' to removal. I would be surprised if most places didn't do that.