Yes, you can but if you are an IIT Aspirant, you should only have a one year gap between passing 12th and joining B.Sc. and applying and aceing for JEE Advanced. In case of JEE Mains, unless you have some categorical advanatage, you can atmost have a 2 year difference between passing Class 12 and Aceing JEE Main, taking admission in NIT or GFTI.

However, I believe if you are seriously interested in pursuing JEE, you need to prepare with full dedication and determination and should waste your time and money by enrolling yourself in a B.Sc. course. Instead, you should invest in good preparation material or coaching institute and Test series and study seriously.