It's possible it could help but it wouldn't be lead to a typical clean DP problem, because you need the full mixed strategy vectors at each level. That requires N real numbers that sum to 1, for each player.

Assuming you've found such a strategy for N, when you go to N+1 you still need to find the (N+1) element vector representing the probability that you select each number as your first guess, and you likewise need to know your opponent's probability vector for adversarially choosing a number. Once you guess at those vectors you can use your recursively built up DP sub-solutions to get the value of the game, but you are still stick with solving the optimization problem of finding those mixed strategy vectors for N+1, and will probably need something like CFRM or a similar technique to find them.