I've actually tried this, after about 10 shots of tequila. Not sure I could handle the pain with any less, especially on the upper lip...
While I did get like one ingrown hair, the biggest problem I had is that you have to let it grow out long enough for the epilator to grab. Also, it doesn't look quite the same as regular beard stubble when doing the growing out. I did it again like 4 days later, but I don't see how this could really work if one wants to leave the house everyday en femme.
It may destroy some of the hair follicles at the root over time, but it would be over a very long time period, like decades...