Can MacDrive break my Time Machine backups?
The short answer is Yes.

If the Time Machine drive is accessible to Windows (via MacDrive or anything else), then it can be corrupted and directly destroyed.  For this reason, I recommend turning off your Time Machine drive while in Windows.

Another possibility is that modifications to your primary drive could cause its ID to change, which would break its association with its existing Time Machine backups.  The old Time Machine backups would still be there on the backup drive, but they would be treated as being backups of a different system.  It sounds like this is probably what happened.  It could be because you (or something) renamed the primary drive or otherwise tried to change it at the root level.  But since you saw a MacDrive error, its more likely a glitch in MacDrive.  There's not much you can do to prevent that except not use it.

Try running a Disk Utility check on all drives, preferably while booted from a DVD or an external drive.  That will at least make sure nothing worse happened.