To answer your question simply, yes a sub 12 FPE rifle will work for beyond 50 meter shooting.

To fill in the answer a bit, you'll need a good scope, a set of high mounts would probably be of benefit for the longer ranges. A sub-12 FPE 22 requires more finesse at the longer distances due to the more parabolic trajectory, but it's doable. As an illustration of what can be done with "less than optimal" pellet launchers, a few years ago I used my Baikal IZH46M 10 meter pistol to shoot a group at 50 meters. The wadcutter pellets were running around 300 fps, if I recall correctly. Power was down on the pistol which was needing a rebuild Anyway, by holding up a portion of the barrel in the rear sight, using the top of the target backer as a reference point and shooting from a rest, I managed a three shot one inch group that day. I'm not saying I could do it again, but the conditions lined up just right and I was tickled pink with the results. The pellets barely broke the front part of the corrugated cardboard target backer and were stuck right there. If an underpowered target pistol can reach 50 meters then your sub-12 FPE rifle can reach way out there as well. Give it a try.