No, his son still would not be eligible as a Qualifying Child for you to claim because the his son is not related to you.
The other option is if his son could be claimed as your qualifying relative, but for that his son would have to live with you the whole year.
If you were married and filed a joint return, the situation would be different. But since you are not yet related to his son (you will be once married) at this point you can't claim him.
It might seem like, if you can claim the fiancé, you should also be able to claim HIS dependents, but it just doesn't work that way.
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