I mean, for smaller routers that had static routes set for that subnet, it would probably just keep working - the issue being that trying to get to real addresses in the 1.0.0.0/8 network (or parts of it) wouldn't work.
If you were BGP peering then you'd probably get a real route into your local table though.
So yeah, some stuff would probably have just broken, but that's the risk you take using parts of the IP space you shouldn't be using!
