CNN combined with a competitive search algorithm

I'm reading some papers about Deep Neural Networks applied for board games, like for Go with AlphaGo, AlphaGo Zero and some other games, like Othello and Chess. Most of the works are using CNN's as a direct move predictor. I want to make some experiments using Tic Tac Toe to implement a CNN, but I want to combine Deep Learning with a competitive search algorithm as Minimax or Alpha-Beta Pruning (CNN will be a "heuristic function" or evaluation function to the search algorithm). In this way, each leaf node generated by the search algorithm will be a input to the CNN, which will output a numerical value between -1 and 1 (values next to -1 means bad position and values next to 1 means good position) and return to the search algorithm. So, such approach makes sense? Is there anybody who tried something like this?

Thanks!