No he shouldn't
How could he possibly get in trouble? Go ahead and tell him. The big test will be to see if he stays with you.
NO... the Navy doesn't care about your sex life.<br />
He might wonder how you got pregnant a week after he left!<br />
Your parents & his parents might give you both grief.<br />
I suggest that you both get married soon, so that you & the baby can be on his Navy Health insurance and receive benefits you won't get otherwise.
If you don't you'll get in trouble