Honestly its a question that only you can answer because of the specifics involved both for you personally and also professionally. I've contemplated it myself and I will probably end up going in a couple years after I stack a few more years of management experience cuz as your father has told you work experience trumps a piece of paper.
However and this is a big one, at least from my understanding and talking to other MBA grads, if you are thinking of switching careers it can be key, the exposure to different people in the MBA program can be vital in introducing you to a network of people that can help in switching careers. Of course it does apply to your current field but honestly speaking if you are climbing the ladder currently you're most likely gonna hurt your progress in the short run and you will inevitably meet colleagues in your current field at work.
This is the aspect Im most interested in. Ive been in risk management at a commodity trading firm and have gotten to middle management but this isnt what I really wanted to do, Ive always been more interested in investment banking or even asset management, the current people I meet are all energy specific so it doesnt help me in getting into that business.
The only way I see myself getting into that field is with an MBA and getting lucky meeting the right people.
Btw is your firm accepting resumes?? haha
You are in a special predicament because the cost issue is not a problem which is a pretty great situation to be in, but I dont think just because you can have it paid for that it should change the need to have one.
In the end you are still young, im 30 and im thinking of doing all of this in a couple years! theres no rush it will always be there and the work experience you stack up will be invaluable with or without an MBA.