I'm not sure that they could discharge you for it, but you would definitely be looking at mast, a bust, etc.
My advice is that you stick it out. You both volunteered. I'm willing to bet you're both still in training. Not many jobs pay your medical expenses then put you behind a desk for a year after you’ve had a baby.
With you being preggo, you'll end up with LIMDU orders to wherever you are. He, not being preggo and being physically fit enough to transfer, will be transferred on time to his next duty station.
If he chooses to go UA/desert he will either go to mast or be (likely) OTH discharged for desertion. This places his future earnings (the $ for the baby) at serious risk. If he goes UA and you know where he is, harbor him, and do not report him you will very probably be busted down but kept on active duty. You will have successfully cut your joint income by 75%, he will go to the nearest brig when found, you will be making doctor’s appointments from the restricted barracks for two months.
For you, UCMJ article 78 (accessory), 81 (conspiracy), 92 (failure to obey), and you're probably going to lie for him so 107 (false official statement).
For him... 81, 85/86 (desertion/ua), 87 (missing movement, if his unit deploys), 92, and 134 because training commands like to toss that one around. If he deserts, brig. If he goes UA, restriction and he remains on active duty. After his restriction time they'll probably get in touch with his detailer and send him someplace really nasty.
So to answer your question... If your command is threatening to punish you according to violations of the UCMJ which you will be guilty of, it's not an empty threat.