Does coffee really interfere with thyroid medication absorption?

Yes. Yes, a recent study done by an italian group and published in thyroid journal showed up to 35% reduction in thyroid level absorption if thyroxine was taken with coffee.
Yes. Ideally wait 2 hours before having any food or drink after taking your levothyrixine. You do not have to take it in the morning however. Pick a time of day that works best for you, for instance- before bed (just wait at least one hour after your last meal).