They'd always lose if they broadcast it after another pool has found a block unless they were big enough to get two blocks back to back.
Not necessarily.
It would depend on how well connected they were to other miners and pools, and how well connected the pool that found the block was.
If they received the block directly from the pool that found it, and then immediately broadcast their own block to all the other pools before the competing block had propagated, then they'd have a pretty good chance of winning.
Anything's possible, sure, but since
they have to receive it from the other pool and then broadcast their own, then every other pool may also have received the block. Sure they might be the only pool with a good connection to the one pool that solved the block but there is no magic to make one pool substantially better connected to
all pools than all other pools might have. Too many ifs and buts, but yes in this pedantic world, my ALWAYS is indeed wrong. Let's say 99% to not leave any absolutes out there... Either way it's far too risky to likely lose a whole block reward.