Programmatically, no, but I've made about 1500 puzzles and been sharing them with friends for months and neither I nor anyone else have found a double solution yet.

It would happen if I picked generic clues like BR/SL/ER (not a real puzzle, don't try to solve it), but I make a point not to. As long as you pick clues that are a little more specific than that, it's actually extremely improbable, despite what you would intuitively think (I had the same thought in the beginning!). Remember that there are 4 restraints, not 3 - it has to match 3 different prefixes or suffixes, but it also has to only be 3 letters (4 letters on weekends).

Sometimes I'm suspicious and I do verify them, but it's really only a risk with the compound word versions like SELL/LAW/FOX. Those I have to be more careful with.

I'll point out that 26³ is only 17,576, so brute-force checking that there is only one solution for a given problem shouldn't be computationally difficult.