Technically yes, you can appear for NEET without NCERT. But:

NCERT books (especially for Biology, Chemistry, Physics) are the base of NEET syllabus

90–95% questions in NEET come directly or indirectly from NCERT

If you don’t study NCERT, your chances of scoring well become very low. It’s highly recommended to study NCERT books thoroughly along with your Maharashtra Board books.

NO, as a student from Maharashtra board you can't give NEET exam without studying from NCERT books because it's going to be very difficult for you to score well.
NCERT is very important for NEET exam because NEET 85 to 95% syllabus is based on NCERT books from where question comes directly and indirectly. The main subject is Biology that is entirely NCERT based.
You need to read NCERT books of PHYSICS, CHEMISTRY, and BIOLOGY to score good in your exam.