Yes this is reasonable. However, since the number of epochs is just another hyper-parameter, the CV results will be slightly optimistic compared to the one you'll see in your future data. This is because you've used the 'epoch' number that was optimized for each fold.
In order to calculate the 'actual' CV score, you'd have to use nested CV. So, within each fold of the outer CV, you do a new inner CV procedure which you use for finding the 'average' epoch number. Then, you use this figure to train the fold of the outer CV. You repeat this procedure for all outer CV folds. This way, the final outer CV score will not be 'overfitted' to the train data.
EDIT:
Pseudocode for nested CV
for outer_train_set, outer_valid_set in train_set(K_fold):
for inner_train_set, inner_valid_set in outer_train_set(K_fold):
Train NN and find the optimal #epochs with early stopping based on the inner_valid_set
Train NN using the average #epochs found on the inner loop
Evaluate performance on outer_valid_set
This nested CV procedure will give you the optimal hyper-parameters (if you don't already have them) and will show you the expected error (e.g. log loss, RMSE) that the model will have if you use the average #epochs of each fold.
The final selection of #epochs can be either the average respective figures of the outer folds or the average of the figures in the inner folds (if I'm not mistaken, these two figures should be the same).
