P-value using Gaussian Discriminate Analysis

I was wondering , in Gaussian Discriminate Analysis (GDA) model, say we have two classes to classify y=0 and y=1

So after fitting the Gaussian over y=0 and y=1 dataset, when we try to predict class label for a new test data point, It says it uses the Bayes rule to calculate P(Y=0/1 | X) and assigns the class having maximum probability.

My Query is can we use p-value instead of Bayes rule to test if the new data point belongs to y=0 or y=1, since the distribution we fit is Gaussian.

Hence p-value will tell probability of seeing the test data point for both the Gaussians (for class y=0, y=1)

So Is my understanding correct and can we use p-value instead of Bayes Rule ?