No. You'll still want to wait the alloted time between taking Synthroid and taking another pill. I had a sinus infection since being on a thyroid med and woke myself up earlier to take it, then went back to sleep. When I rewoke I'd figure what would be four hours (the recommended time told to me) and take the antibiotic then.
Good luck. Hope the antibiotic is for nothing too serious and that you're feeling better soon.
oops ... I mean "I now have a round ..."