Re: appointment tomorrow!!
Taking the med will skew a free T4 reading, making it appear higher than it actually is on average. (It won't affect total T4, TSH, nor anything else.) To be on the safe side, I'd take it after the blood draw or perhaps just skip it altogether. One day's missed dose won't make a lot of difference in the long haul.
"We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses." Abraham Lincoln