Yes you can, I did it. I was an EP-3 NFO for my first tour and I was lucky enough to get a transition to EA-6B's at the end of my first squadron tour. I knew several guys that wanted to transition but lost interest after getting to love their first airframe. I loved my tour in VQ but I wanted a little more excitment than sitting sideways in the back of a tube staring at a computer screen (I got to stare at one facing forward, with a G suit, harness, survival vest and helmet this time!). I had to go back to flight school, advanced jet training, and then to the RAG like everyone else.
I can tell it you it is not easy. I did well in my first squadron and happened to be in the right place at the right time. I had a lot of fun though until they decommisioned my squadron

, but it was well worth it. It will be more difficult to do it nowadays with the S-3 going away, they are taking up a lot of the extra slots. They are sending them everywhere including VFA, VAW, VP and VQ. It is apparently take it or leave it. I have not seen a regular transition board come out in a while. Most of the F-14 guys are going straight to F/A-18F's. With retention sky high in aviation right now, it is even more difficult (VAQ is overmanned).
Most of the people who transition are pilots, I have only met a handful of other NFO's who have done it. Wink was right when he said it is not the best for your career, you are an oddity and that is not usually good. It also depends on hthe community you go to, VAQ is generally more accepting of transtitions than VF. I did it to keep flying and have fun and have not looked back though. I have had a blast.