Absolutely!
I'm a depper myself. It is a wonderful option because although a recruiter may not tell you for fear of you choosing to do it, you CAN BY LAW drop out of DEP anytime before you ship if you change your mind. The only repercussions of this ELS (entry-level separation) are that you may only be able to join that particular branch or any other branch under certain conditions which they specify.
It is frowned upon of course because of the great amount of money that is spent for you MEPS medical testing, job reservation, ASVAB, etc.
If you want something different, want a change, want to travel, want life experience, want a challange, want to grow as a person, meet others and mold yourself into a proud and mature person of character, then the Navy (or probably any other service) is ideal for you.
If you haven't already contacted a recruiter, just go see/call one, tell him why you want to join, what you want to do and get out of it and see if you are mentally/physically/morally qualified, and he will send you down to MEPS, get you enlisted in DEP, and get your ship date.
Good luck, and welcome aboard! (wish I could say that as a true sailor, but I can't call myself one just yet)