Is it possible to use a single Time Machine backup so that two Macs are always in sync?
Time Machine is not designed to do this. It will not make bootable backups, so you can't use a Mac as a destination for backup (and have this backup be "functional").

There are other solutions for synchronizing multiple machines. If iCloud/Dropbox/Google Drive type solutions are not sufficient for your needs, there are other tools that can sync - Chronosync is one solution.