You will still have 240V going to the element itself it just won't be causing the element to heat up. Make sure the dryer is unplugged, take the back off the dryer and pull the element out. It's usually just a few screws. Mark and write down what wire goes where. The wires have clips that will slide right off the element, take it to your local hardware or appliance store with the dryer info and put it back on in the reverse order. Elements are usually pretty cheap.
If the motor is 240V, then yes. It really depends on the dryer and what voltage devices are used inside it. If the dryer includes a motor to drive a fan, the motor may actually run at only 120V. Since the manufacturer has two possible voltages to work with, it can install whichever kind of motor is cheaper.
As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.
If you do this work yourself, always turn off the power
at the breaker box/fuse panel BEFORE you attempt to do any work AND
always use an electrician's test meter having metal-tipped probes
(not a simple proximity voltage indicator)
to insure the circuit is, in fact, de-energized.
IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS
WORK SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.