The answer is NO. Or let's say, not really.
I have talked to 2 supervisors that hired me and asked that same question. They look if you have the licenses they need; CRT, RRT, PALS, BLS, ACLS and any other licenses from the NBRC. Then they look at your experience. If it is more specific to their needs, they will call you for an interview.
If you are referring to new graduates, say 2 people graduated today and one has AAS and the other BSc, then both of them have the same licenses. Well, there is honestly no advantage there. The hiring person calls people who are considered potential candidates to be hired.
Now, when you go for the interview, it depends on how well you interview. If you have a BSc, better impress them with your knowledge and attitude. For at the interview, they really are not attracted more to your BSc, but to how well you handle yourself and express yourself.
So, my experience and knowledge has shown me that if you have BSc, it does not increase your chances of getting hired.
BUT!!! BUT!!! In the future someday, I believe everybody would be required to have BSc in Respiratory to work in the hospital. Same reason why you see now the CRT seems to be fading out.
A lot of people are getting themselves very educated these days, and more hospitals are wanting their licenses employees to have BSc, where their programs offer a BSc. So, that is why I believe so.