You should be good to go. Coopers as a breed tend to shoot, though in my experience expensive rather heavy rifles better shoot or what's the good of them? I only have two Coopers.
The 270 Weatherby cartridge itself is nothing to be sneezed at; when we were all stroking a boner over STWs 30 years ago with light bullets and MPBR with light bullets it required a bit of willful blindness to not see that Roy was doing it in the 40s.
If you want to go to what most people would consider extreme long range with a 'Bee you may have a bit of an issue with high BC bullets and a long throat, but that's sort of a specialty application. I had a lot of fun scratching down goats by the 100s in NZ out to 800, but you might have to pick your bullet carefully for your own rifle for that. Or maybe it doesn't apply at all for your uses.