Full Time MBA at 33 - Does it make sense ?

Hi, I am looking to completely transition from my role as Individual contributor and Software developer to a complete Product Management role.

I have tried transitioning internally but its not happening.

I joined a PSB recently from Private IT, but it's not suiting me at all.

I am exploring quitting my PSB Job and enrolling to a Full time 2 Year classroom MBA program, if I am able to crack a good CAT score.

I have FMS in my radar because of it's low course fee.

Is this a good idea ?

Post a Tier 1 MBA (if I am able to crack that), will Product Management roles open up ? What specialization should I look for ?

I am also interested in FINANCE, but I have zero experience in Finance, so I don't think it will be a viable option.

Current CTC (on paper) is around 25 LPA and total experience is 10 Years in IT Industry.