Aside from the frankly strange situation that would be (you don't just hand source code over to a platform holder), just having source code doesn't allow you to make arbitrary changes. You need to compile source code into a brand new binary for it to do anything, that's a whole development process that wouldn't be remotely in the scope of their BC team. The only real chance the Xbox BC team would have is if there's some plaintext config file they'd be lucky enough to hijack or some weird quirk in how a games vsync worked (this happened exactly once).
If 60FPS patches were to happen on that scope, it'd be far more likely it'd be up to the original studio to submit patches for with some kind of alternative SKU or an OS environment detection added to the API for the studio to added to their code. However even if that happened adoption would be super low, these are ancient codebases with equally ancient Middleware licenses, there would be a non-zero number of games that would need to renew licences just to compile a new build, assuming they even still had working project files, tools, or even source code that hasn't suffered substantial archival rot.
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