I haven't been to BRU recently, but previously at BRU, if you're arriving on a Schengen flight you get dumped in the Schengen part of the terminal. I don't know what happens if there is a bus gate involved (or if there are currently bus gates for Schengen flights).
There's one other thing to consider - you can't be 100% certain that the plane to Alicante will be the same plane that's coming from Alicante. There may be a rotation of planes, or if it is the same plane, in case of mechanical delays, etc., they may find another plane to take the route.

There's one other option - leave the keys in a locker either at BRU airport or at a train station. Most lockers nowadays require a barcode or QR code to retrieve the contents - usually it's printed on a piece of paper.