Yes. MGS is equipped to handle such tasks. But that won't do much good. MGS has too low of a resolution. A few groups out there think MGS may have photographed the polar lander crash site and debris, but its only a few pixels of data. Beagle is much smaller than the polar lander, so you're not going to find anything.
Odyssey might also be able to pick something out in other bands, but it probably has too low a resolution also.
Mars Express has a 10-meter resolution camera, and can zoom to 2-meter, but if Beagle's in pieces, 2 meters is low.
I can't tell you the resolution of MGS or Odyssey because JPL's mars missions page is down for everthing other than the rovers.