"If I go Start, My Computer, Drive C, right click, Format, will this clean the drive completely?"
No - that would wipe out the OS that the computer is in the middle of using - so it can't be done.
If you install Ubuntu it would reformat the system with a different file system anyway, so you don't need to reformat first.
Linux may be able to run the games using Wine, which sets up a pseudo-windows facility to run windows programs. No guarantee that it will work with those particular programs.
Or you could install a virtual machine under Linux, and run a windows version in it - if disk space permitted.
In 256MB RAM it may be better to look at Xubuntu or even Edubuntu, which are lighter on resources. I recently built an old system for a friends youngster with Edubuntu, and it's been a great hit.