Retrain final layer of Inception model
The short answer is yes.

While your classes are imbalanced, model will be more likely to "learn" class 2 during the training, especially when it comes to mini-batch updates. (even though each mini-batch is unlikely to have only class 2 samples)

The common solution is to use weighted loss function or feed weighted samples to mini-batch.

In my practice, I always use weighted samples if I have sufficient data, even when my classes are not that skewed. Weights always help, at least it never ruins the model.