In my belief, generally no, since the thyroid med will cause a spike in your levels right after you take it and they'll read the spike and not what is left from the previous day (i.e. how much is left?). The doctors don't say too much about this either, usually, so that's been the generally accepted rule as far as when patients talk about it.
I noticed at least as far as TSH goes a 2-3 pt difference depending on whether you take it BEFORE you get tested or AFTER you get tested. I usually go in the morning to get tested anyway, so I neglect taking the thyroid stuff until AFTER I get tested.