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.