Yes it'll work. The "conditioner" is just a mix of food-grade mineral oil and beeswax. You'll probably want to apply several coats, per the instructions on the bottle. Just note, that stuff isn't a permanent finish, so you'll need to reapply it periodically. Washing with hot water will make you need to reapply it ore frequently, due to it taking the wax out of the finish. You may want to get just mineral oil and finish with that, first, as the wood you used is fairly porous, and you want to have the wood soak up as much of that oil as possible.

Source: I use that stuff on my own cutting boards.