Can I back up my iPad with my time machine?

No, iPad backs up to iTunes on your Mac.....or.....to iCloud.

If you backup to iTunes on your Mac.....when the Mac backs up using Time Machine....the backups of your iPad will be backed up as well.

More info on iOS backups is here:

How to back up your devices using iCloud or iTunes - Apple Support

If you back up your iPad with iTunes, and back up your computer with Time Machine, then the iPad backups are backed up with Time Machine.

Technically the backups are in stored within the iTunes folders, but if you back up your computer, Time Machine will back up those files as well.

There is no way to ONLY back up your iPad with Time Machine. Not sure if that is what you are asking about or not. Time Machine is designed to back up your entire computer, not specific iOS devices. iTunes is designed to back those up.

Hope that helps