Should insulation batts in my attic be lifted off the ceiling, leaving a gap?
Sounds like a sloppy install to me, and as a result the insulation that's not in continuous contact with the ceiling panels is doing nothing. If air can circulate around the insulation, virtually no heat is retained or blocked (in winter and summer, respectively). If this was some sort of intentional air gap there would also be an air barrier over the insulation (out of necessity). 

I would do my best to lay and fit the batts that are there, then I'd consider overlaying blown cellulose (an easy DIY job) to fill voids and bring your R-value up to modern standards.