I agree a lot with what a previous poster has said about focusing on getting through school. However, I also felt as you did at the beginning of Nursing school that NICU was probably what I wanted to do. As you know NICU is a specialty, and as such, is often harder to get hired into as a New Grad. I did some things during school that helped me get my New Grad NICU job.
1. I did my peds rotation at a hospital with a large NICU. It was not an option to do this rotation in the NICU, but my clinical instructor was able to get me an afternoon in the NICU where I met some influential people. I told them of my desire for NICU, and my hope to be able to do practicum there. When it came time to request practicum placements, I requested this hospital. In my request I mentioned some of the people I had met there and how impressed I was with the facility/nurses. I got my practicum there and loved it!
2. In my OB rotation, there were some days that I was assigned to L/D when it was just dead quiet. My clinical instructor knew I had an interest in NICU and arranged for me to spend the day there.
3. I did not have the opportunity to volunteer/work in a NICU while in school b/c I did accelerated and simply didn't have the time. However, I worked my tail off in school and got steller grades. Some will tell you that grades don't matter...we all put "RN" after our names once we pass NCLEX, but in this market when employers have their pick of pretty much whoever they want to hire, it is certainly a plus to have those grades.
As for ASN vs BSN, it is probably a little different everywhere. You may want to do some investigating into what hospitals have the largest NICU's in your area and whether or not they hire ASN's. If they are magnet status, you probably will not have a chance. I know some magnet status hospitals that will hire ASN's with lots of experience but never New Grad's. In my area, even the hospitals that normally hire ASN new grads are saying "BSN preferred". The fact is that they can be picky right now.
Honestly though, as you know your focus right now is school. I would go into every clinical placement you get acting as though that is where you want to work. You never know when you may need that job, even if it isn't your first choice. For example, I hated med-surg. I can guarentee you that the nurses I worked with on my med-surg rotations and my clinical instructors would never have guessed that.