register two different IRQs and install two different handlers for the single driver
"It's just that easy". The answer to "is it possible" is "Yes".
Device interrupt rountines will not interrupt each other on the same CPU.
According to LDD3 (this is quite old now), a single interrupt routine could be assured that it did not run on multiple CPUs simultaneously. I'm not sure what was meant by this - I can't imagine it applies to timer interrupts.
In your driver, I would expect it to be possible for the different interrupt routines to run at the same time, on different CPUs.
However the typical "spin lock irqsave" to achieve mutual exclusion where necessary, should still work fine in this case.
You might want to double-check you have the NMI watchdog, and lockdep enabled on your test system :). The NMI watchdog will trigger if a cpu gets stuck spinning inside an interrupt routine.