Hello,
no, anything connecting to the network, will use the IP that has been assigned by the service provider.
Assuming, you can use the proxy forcing feature of Sandboxie-Plus, which requires you to set up one or multiple SOCKS5 proxies and then configure the sandbox to use that proxy, it may appear that connections come from different IPs, depending on how the proxy connects to the target.
It may fail to work, since it may appear that you are connecting from multiple locations, which could suggest that you shared log-in information or that you were hacked and is therefore prevented by Steam. It may fail to start games, since their anti-cheat tries to detect if the execution environment has been tampered with and throws errors if it thinks it is being fooled.