Don Evans
The answer is yes it can, the recip action is all done in the handpiece that you attach to the flex shaft. The SR is just the motor.
There are several rotary tools available that have the handpiece that recips, I've got a MasterCarver that I like a lot better than a Foredom. Biggest problem with Foredom is their over pricing their stuff.
Do a google search for Master Carver and check the price on it, you can find it with a package deal that includes 3 handpieces and one of them is the recip one. You'll find that it is less expensive than the Foredom. Also, any Foredom handpiece will work with the Master as they both use the same type flex shaft. Also, the Master is more horse power than the SR which I believe is 1/6 hp the Master is 1/3 hp and they just came out with one that is stronger at 1/2 hp. It's built like a tank also.
Don