Maybe? It is better and more clinical than my business bachelor's and I got accepted into 2 schools. Obviously, a BSN is more competitive and better for you, but I didn't want to spend the extra time and money on a BSN. I felt that my strong science GPA, GRE score, work experience, blah, blah, etc... would help me apply to CRNA schools - and it did. NOTE however, about <10% CRNA schools accept a nonBSN and you better believe that I applied to them all. Graduate school applications can be expensive, but they were cheaper than the time and money involved in upgrading my Diploma RN to a BSN. Plus, I saved myself the headache of drudging through Nursing theory. God Bless you Dorothea Orem, but my theory on Self-Care is not wasting my time doing extra work when I can get in school with a nonBSN.
Again, NOTE: I have nothing but respect for BSNs, but I didn't have the time, money, or desire for it.
I wish you the best of luck. If you apply to CRNA school as a nonBSN, make sure all your other STATS are excellent.