Every situation is different. To me the oath has significant meaning. My wedding vows, which are in essence, an oath, have significant meaning. In my opinion, the service can make a weak marriage crumble faster or hide problems that may fester for a long time, until things get ugly very fast. A strong marriage will always work if both people are commited. Just my opinion.
In my case, I was struggling to figure out what to do with my life after two years of college and one year of "working". I decided to join the navy. My fiance broke up with me because she didn't want a long distance relationship (I had been working away from her about six months prior to this). I went into DEP. While in DEP, she decided that being with me part of the time was better than not having me around at all, so we got back together (I can't imagine what she saw in such a slacker, but I'm glad she changed her mind because I'm the luckiest bastard on the face of the earth).
We got married six months later (between A school and Nuke school) and are approaching our 24th wedding anniversary, all in the navy.
Back to the oath(s). One of the things taking an oath did for me was provide a basis for working through those problems or diversions that cause people to lose focus on the reason they were joining the navy. In my case, the navy was my last chance (at least I thought so at the time). I had to suck it up. My wedding vows are about the same in my eyes. My wife put her future in my hands (including giving up a full-ride college scholarship). I love her madly and to this day, I can't sleep the night before I get home from sea because I'm thinking of her (and the home from sea "marital relations"). Doing my best at nuke school and prototype were essential to providing the best I could for my family.
Sorry to ramble on, but I think you need to look at why joined DEP and why you need to get married now. If you're afraid of the commitment required to succeed at either, you do yourself, and everyone else a disservice. When you're in nuke school, studying until you can't think straight, and feel like calling it a night because you've made your hours; but you haven't memorized the equations you need to know for the exam tomorrow, will you go home to be with your lonely wife, or will you call her and say, "Honey, I've get to give it another hour so I can pass the exam". Will you recognize that sacrifice now will allow you to have a higher standard of living later, or will you take the road you always took before the navy and piss away another opportunity? If you can raise your right hand and take an oath, then back out of it; why should your wife-to-be believe anything you promise her? The honest answers to these should give you the right answer.
The technical answer to getting out of DEP should be in the paperwork. Your recruiter should be able to answer that, though he will give you an extremely rough time about it.
