I have a .308 Axis and 6.5 Creedmore in Savage 10 neither of which have a break/can, and it is difficult for me to follow shots downrange. Even shooting off a nice bag, or a loaded bipod and practicing good recoil management, 90% of the time the kick is just enough to throw me off where I lose sight picture and have to readjust. I would imagine with a 30.06( I don't personally own one) you are going to have a similar problem.

I think the best solution would be to add a nice muzzle break which should help.