No. In making a lethal shot there are already too many variables so why handicap yourself with a minimal cartridge? Would you hunt a Kodiak Bear with a 30-06 Encore if you owned a .375 JDJ Contender?

And if you only owned a 30-06 Encore then wouldn't it be much smarter to buy a .375 JDJ (or bigger) to help ensure the trip was a success? (I am not sure if a 30-06 is legal for Brown Bear, just a comparison.) I do know a friend that killed a Kodiak with his .375 JDJ Contender in Alaska.

In Colorado and Wyoming and other states the .223 is not legal for big game.