Yes, but the signature would be broken.

But how would this matter in practice?

Signed executables are required on a lot of platforms (consoles and some PC publishing platforms), however, they're only any use if the security of the authenticator can't be broken. On consoles, it's a closed platform, so this works until someone cracks the hardware/OS, but on PC it's not possible to make 100% secure. If authentication is done locally it can be cracked, and if it's done remotely then a local hack can send lies over the network. In either case, you can still interfere with a running program after it's been launched/authenticated.