T4 will suppress the thyroid but not shut it down completely. Reason being t4 is converted to t3 but it is not the sole source of t3 production. Plus T4 conversion to T# is limited. So if you supplement with t4 over time your body would not produce t4 BUT the endogenous T3 production continues. SO your thyroid would be suppressed with extended t4 supplementation but not fully shut down.
Make sense?