Technically, you can. But practically, in this case, you probably don't want to.
TM backs-up whole systems, not just drives and data. If you back up two or more Macs to the same drive or TC, TM will keep them separate. You can view and restore from backups from other machines by holding down the
Option key while selecting the TM menubar icon, changing +Enter Time Machine+ to +Browse Other Time Machine Disks.+ Since your old and new Macs are different machines, this would work.
But there's a problem: since the backups are for a different Mac, TM on you new Mac won't automatically delete the old series in the normal fashion. Unless you delete them, they'll be there forever, taking up space you need for new backups.
Worse, it's very tedious to delete them manually. Do
not use the Finder, but you can delete the old backups, one at a time, via the TM interface. It's a long, tedious process ... and much longer on a TC.