If they’re measuring your thyroid levels only, they will not do a pregnancy test. These are separate tests. The tests they will do are checked off on the lab slip that you will take with you when you go to get your blood drawn. Look at the slip – T4, T3 and TSH should be checked off, these are thyroid hormone levels. There should be a spot for a pregnancy test elsewhere, and it will not be checked off.
If you WANT them to do a pregnancy test, mention it and I’m sure they can add it to your labs. Or hell, just check it off yourself. If you don’t want them to, they will not without you or your doc asking them to – or basically without that little box being checked.
edited to add: It is important that your doc know if you’re pregnant if you have thyroid problems! Simply being hyperthyroid while pregnant can cause miscarriages. Here is more info about pregnancy and thyroid disease.