My animal science degree doesn't translate directly to FAID either, but the core science classes I took (bio, chem, physics, etc), along with those of my major, had given me a strong scientific background on which further training can be based. Use of the scientific method and learning to think like a scientist are the larger points that I got out of it that I use on a daily basis in casework. (this is my canned answer if ever asked in court how a BS in animal science = firearms)
Is nursing considered a "hard science" like bio/chem/phys? I don't have an answer for that; I suppose it depends on the agency that's hiring. Different places have different requirements. Mine, for example, requires the candidate to a BS in a core science. Eight years ago, I had zero idea of how guns or ammunition worked and just wanted to break into the field...but that's what they were looking for...a fresh mind to mold.
Long story short...in answer to your question Charlie, it depends. The science background can't hurt, same goes for taking a proactive interest in the field, such as internships, ride-alongs with police, volunteer work in the field, etc. Good luck!