Computer 1 is surfing the internet while using a VPN and at the same time accesses files on computer 2 (this computer does not have VPN) on the same local network. Since computer 2 does not have a VPN would it somehow reveal the public IP of computer 1 even though it has a VPN?
It is irrelevant that they are in the same network. If the PCs are clean (free of malware, etc), there should be no such issue.
Exception to this is if you use 'internet connection sharing' between them. This combined with default routing distances can cause things to go out through the wrong way.
So if there is no ICS or malware on the computers, everything should be fine. At most, if they both have public IPs, the other IP can be determined if the whole IP subnet is scanned, so one could determine that you have another PC in the same network.