I sealed the bottom of my up and over door in the last house. The car rusted the wings and doors, presumably because the damp air could not escape easily.
The door at our current house is unsealed, and over 40 years we have never had a problem with the cats rusting, or even staying wet.
The brush sealing should be good, in that it will prevent water ingress, it will be permeable, so that moist air can escape.
Failing that, why not a shallow lip inside the door, (Aluminium angle fixed to the floor, say 30 -40 mm high?
Howard