Yes, you will be eligible for MHT CET exam to take admission in private engineering colleges of Maharashtra.

You can also take admission in Maharashtra private engineering colleges through JEE Main and it will be preffered as well.

If you are appearing for JEE Main then there is no use to appear for MHT CET exam.

You can also check the MHT CET eligibility criteria from the given below link

MHT CET Eligibility Criteria

Good Luck!!