No.
Critical elements for conversion of T4 to T3 are zinc, iron, selenium, and iodine. Your body also needs sufficient cortisol to support the conversion of T4 to T3. Cortisol also plays a major role in T3 metabolism. Without sufficient cortisol, T3 will begin to pool in your blood and further conversion of T4 will likely end up as Reverse T3 (inactive thyroid hormone). Reverse T3 fits into the same receptors as T3, getting in the way. When Reverse T3 levels are too high (otherwise known as Wilson's Syndrome), your cells will have less T3 available to them. This will cause a down-regulation in metabolism similar to hypothyroidism.
If you were interested in supporting the conversion of T4 to T3 as well as the increase in metabolism from T3, I would recommend pregnenolone. Optimal levels of pregnenolone will support neurotransmitter function and help to raise coritsol levels, helping T4 -> T3 conversion and metabolism. It will likely provide an increase in DHEA levels as well.
Steroid hormone conversion pathway:
1. Cholesterol->Pregnenolone->Progesterone->Cortisol
2. Cholesterol->Pregnenolone->DHEA->*sex hormones*