I've done that quite a bit on table legs, and also on chair rails, where it's often hard to get the thickness required to cut a suitable arc without compromising the integrity of the wood due to grain direction. I've yet to have a problem.
I've also "laminated" the sides of casework with two thicknesses of wood with what I think is success, but it may take another 100 years to prove that.
About the only caveat I would recomment is to consider trying to match the "cut" of the wood ... i.e, flat, rift, quarter, etc.
Mind you, this is my experience and I like to experiment, but in that experience, as long as you stay "long grain to long grain", with roughly the same dimensional instability characteristic of your stock, you should be fine.
This should keep you in the ballpark on the latter: