Could suspend in Condor DRMAA be implemented with checkpointing support?

It is already. Due to the usage of "condor_hold" for the implementation of the suspend operation, the job is 
checkpointed in standard universe, and cancelled in vanilla universe. You simply need to tell the Condor DRMAA 
implementation which universe your job belongs to, as described in the library documentation.

Related question.  Is there checkpointing under Condor that does not require recompilation with Condor tools?

No. This would demand some kind of operating system support, which is not available in the aimed platforms (Windows, 
Linux, ...)