Can a billing dispute with my bank impact my service?

I requested a payment reversal about 60 days ago, and T-Mobile has failed to rectify the situation despite claims that the refund was added to my account the day the reversal was requested. Despite contacting T-Mobile and my bank on multiple occasions, there is no refund in my checking account. 

I've tried multiple times to get the issue fixed, but nothing seems to be working when I go through T-Mobile, so I'm considering going through my bank. My only issue is that I am worried this can impact my service if there is a chargeback on my account. Is that possible?