You may find you don't have enough clearance for a rear wheel+MTB tyre, my StumpJumper 26' is really, really close to the frame and I wouldn't have a chance to put a 29 wheel in there, never mind with a nice winter set of tyres (Nobby Nics). Overall, I'd advise against it. 'I want something with larger volume tyres', I'd recommend just buying some beefy tyres rather than mess with the frame geometry.
My guess, is it will push the bike higher up off the ground, and depending on bike and fit, cause problems with standover height. I also imagine it will push the front end up and make it handle like a tractor, even 29 specific frames sometimes feel this way, and it's not nice. I don't see a harm in trying, but it would be worth measuring up clearances (inc. tyres), how much more the front end will be pushed and overall ground clearance. I know it's only 3 more inches, but it could cause problems.