First, you need a T-Mobile account. I presume that you do.
Second, look at this piece of not so fine print. I underlined the amount you need to add.

Autorefill: With Autorefill, you have a set amount between $10 and $150 withdrawn from your bank for your T-Mobile refill. Schedule when your payment is made:
Monthly: Every 30 days, recommended for monthly plan types.
Every two weeks: Same day every other week.
Weekly: Same day every week.

At it's best, this will only give you 4 transactions (maybe 5 on one or two months a year) using the weekly method.

So, yes, it will work but will it be frequent enough and is the amount withdrawn ($40 minimum/month) low enough to justify the checking account you are looking to acquire?
I'd rather pick up a pack of gum at the drugstore while getting my VGC and use the debit card there.
Cheaper and more frequent