Yes, you can bypass the heater core. I did it on my '68 Mustang for a Summer, while deciding how deep I wanted to dig in addition to a new core. The difficulty in changing out the core is in getting access to it in the cabin. Once you can get to it, the swap is easy.
Craig and Carol
1997 34' Excella 1000
1970 27' Overlander, International
2009 Ford F150 5.4L
ProPride hitch with 1400# bars
Past President Southeastern Camping Unit (12)