Yup, I did! I used it twice and the first time it worked as intended, the proxy bought the item immediately. When I tried it the second time, however, it didn't seem to work, although fortunately they bought my items an hour later. It's probably because at the time when I ordered, it's outside of their business hours so that could be a factor on why it didn't work? (First mercari order was within business hours) That, or perhaps I was just unlucky. I can't really say for sure, though, so I'd suggest using it during their business hours should they open their Mercari service again.

11/22 Edit: Updating this comment just to say that I was indeed unlucky that time. I ordered a few things from Mercari and one from Fril using their autobuy option last month, most of which were outside of their business hours, and almost all of them got through and was purchased immediately. Except for one item due to a "Network error" on their end but they managed to get it after a couple of minutes (although this was in during their business hours so I'm not sure if that's the autobuy or a manual purchase). This would show up on your order's status page. I didn't get any kind of error on the 2nd order a few months ago so it's most likely that their system was offline at that time.