I have the same rifle, but in 270, and recoil would be a bit much for my wife, especially from a bench. The 30-06 will have similar recoil to my 270, but of course it all depends on what weight bullet you are shooting. The A bolt is a relatively light rifle so it will kick pretty good if you use heavy bullets. But I think you'd be fine with possibly the 150's, or even better, I know Federal has a 125 grain load. It wouldn't be one you'd want to shoot elk with, but I think it would be fine on deer, especially if you're not talking about really long shots. Federal also has the 110 grain Barnes, now that would really be a good on to try. I wouldn't be afraid of shooting elk with that bullet, and recoil would probably be about like a 25-06.
I would go ahead and get that rifle if you can get a good deal on it. It sounds like a perfect set up with that 3-9 Leupold scope, and you won't get a rifle more accurate than the Browning A bolt.