I see no reason why not. The board is designed for mounting on top of an Arduino by itself though, so you'll have to mount it separately and run wires to it from the Pololu sockets on the RAMPS. You will also need to supply it with a logic supply (+5V and Ground), apart from just the step/dir/enable lines.
Notes:
Each time you double microstepping, you need to send twice as many step/dir pulses. If you want to keep the same speed as with 16x drivers, this means the Arduino needs to do almost twice as much work (in a set time period). Given that 32x seems to be pushing the existing speed envelope (from what I've heard from people who have pushed these limits) you may find that using step/dir control with higher microstepping values using an Arduino Mega requires that you slow down your moves.
Also note that the more microsteps you use on the extruder, the slower it will extrude (depending mainly on the extruder type, filament size & nozzle size, as that determines the volume of plastic that comes out the end for any given extruder movement), so you might need to play with your microstepping to get plastic extruding out the nozzle fast enough to keep up with your moves. If you can't extrude plastic fast enough to keep up with moves, your object will not print right.
Given you're doing a Delta, you may find it OK, but you do want to look at something faster (like a Due) for control. I don't know if this shield is 3.3V compatible though (which you'll need to be if you want to run off a Due, RADDS doesn't change the logic levels, nor does RAMPS-FD).
Note: For X/Y Cartesian bots, Z really doesn't need that great a microstepping, as you're driving it with a screw-thread.
Notes:
Each time you double microstepping, you need to send twice as many step/dir pulses. If you want to keep the same speed as with 16x drivers, this means the Arduino needs to do almost twice as much work (in a set time period). Given that 32x seems to be pushing the existing speed envelope (from what I've heard from people who have pushed these limits) you may find that using step/dir control with higher microstepping values using an Arduino Mega requires that you slow down your moves.
Also note that the more microsteps you use on the extruder, the slower it will extrude (depending mainly on the extruder type, filament size & nozzle size, as that determines the volume of plastic that comes out the end for any given extruder movement), so you might need to play with your microstepping to get plastic extruding out the nozzle fast enough to keep up with your moves. If you can't extrude plastic fast enough to keep up with moves, your object will not print right.
Given you're doing a Delta, you may find it OK, but you do want to look at something faster (like a Due) for control. I don't know if this shield is 3.3V compatible though (which you'll need to be if you want to run off a Due, RADDS doesn't change the logic levels, nor does RAMPS-FD).
Note: For X/Y Cartesian bots, Z really doesn't need that great a microstepping, as you're driving it with a screw-thread.