The long throat problem seems to be limited to the WSM cartridges, not the standard cartridges, and not even the regular magnum cartridges.
An article was once written that compared a Tikka T3 and a Savage, both in .270WSM. The Savage's velocities were within the manufacturer's expected and stated muzzle velocities. However, the Tikka's velocities were about 200 fps slower. Similar results have been posted by some of our members that had WSMs, and they were very upset. However, I have not heard of any such problems with loss of velocity due to long throats in non-WSM cartridges, so you should be just fine.
One of our members has a Tikka T3 in 6.5x-55 and, if I recall correctly, the velocities were where they should be, and it was very accurate. I can't make any guarantees, but from what I have heard from our members, you should be fine.
Zachary