Should I email a potential supervisor who agreed to support me?
Yes, in general it's entirely appropriate to remind faculty members about letters/recommendations/paperwork they've previously agreed to.  

In fact many faculty members I've known (and I cannot, alas, wholeheartedly exclude myself) rely on such reminders to a greater or lesser extent.  Faculty nowadays are faced with so much paperwork / routine correspondence (and are not necessarily trained or culturally aligned to regard such things as being important) that we start to believe also in the converse: what we have heard about once and never been reminded of must not be very important.  

Just now I got a second email from a secretary in my department about an annual inventory issue.  She sent the first email just a few days before and included a hard deadline in both emails. In other words, she knows all the tricks to get faculty to do things without causing resentment.  The keys: be polite but persistent, and make the convergence to the deadline clear by ramping up the email reminders accordingly.  It really works: pardon me while I run down to her office so she can tag my laptop!