The Navy is a life changing experience. You will be moving in one direction while your guy remains the same or goes in another. Just something else for you to consider.
Back to your question. If the felony conviction of your guy was associated with the sale or possession of drugs, in all likelihood he will repeat, especially if you are not there to keep him straight. The last thing you want is to be in the Indian Ocean wondering if or when your husband will revert to his old habits and get busted. If he does you will too be investigated.
As far as your security clearance goes, your continued association with this guy will raise flags. While confidential and secret clearances are record checks only, they will find out about his history. As was previously pointed out on this forum, your judgment is one of the main points of interest in the background investigation. In my opinion, continued association with a convected felon questions your judgment. Whether that is enough to prevent you from getting a confidential or secret clearance, I do not know. I do know there would be some real hard questions to answer to get a top secret clearance.
Now for some more downside news. It is quite possible your association with him has already caused you a problem. Unfortunately, because the background checks are not started until you have actually entered active service, there could be a big surprise awaiting you.
My advice is for you dump this guy and move on, or minimally wait until you make E-4 or E-5, to make the wedding decision, if there is still a decision to be made.
Sorry, but life is not always fair.