Short Answer: yes. If they could not, they'd likely not get certified
One engine can drive both prop rotors.
After digging into an old version of the V-22 flight manual, I find a whole pile of tables in the chapter that cover single engine flight. Gross weight and DA and flight configuration informs what the "best" airspeed is for single engine flight.
The general approach to single engine flight to a safe landing is to fly at a particular configuration and airspeed, and to set up the aircraft for an approach to a run-on-landing "between 55 and 65 knots." As I understand the procecures, that final approach will have the nacelles tilted up far enough to prevent the tips of the prop-rotors from striking the ground once the aircraft is on the ground.
Flight Safety Note: I am not going to replicate (cut and paste) these procedures here for a number of reasons, on of which is that I am referring to an out-of-date manual, and some of the details may have changed. I suspect that the current procedures are similar.
Note on the source:
An old version in the A1-V22-NFM-000 series; Part V/Chapter 12; Emergency procedures. (There will be a similar section in the Dash Ten for USAF CV-22's).
Where a run-on-landing is not achievable, the manual calls for an approach to ...
... maintain the highest suitable air speed until deceleration is required for a no-nover touch down.
This general method is very similar to the single engine procedures that we had in the SH-2F and the SH-60B helicopters that I flew from ships in the Navy. The aircraft's Gross Weight and the Density Altitude of the day will lead to some variations in the "best" airspeed for this; there are tables in the manual (and usually in the pocket checklist) to determine the best airspeed to fly.
A shallow approach into the wind maintaining 30 KCAS until right before landing is recommended.
This is a little bit different from how we did this, and taught this, in those two helicopter models; we would try for a constant angle of descent approach (not a shallow approach) to a spot if we, as was usually the case, did not have single engine hover capability. The resulting landing would be fairly firm, but that was by design.
Not only is single engine flight possible, as well as single engine approach and landing in a tilt rotor, it's a well known flight characteristic that has well established procedures to accomplish. (At least for the V-22. The AW609 doubtless has similar procedures in its flight manual).