No, unfortunately, if you want to give an improvement exam for your class 12th HSC boards in July and want to participate in the current year's Maharashtra CET (MHT CET) cap rounds, it likely won't be possible.  MHT CET eligibility for cap rounds typically requires you to have passed the qualifying exam (Class 12th HSC) before the start of the admission process.

MHT CET : https://www.careers360.com/exams/mht-cet

I hope it helps!