It is absolutely reasonable to split the dose, especially if using Armour Thyroid or other T3 containing products. You can take the second dose any time four or more hours after the first dose. This is especially helpful to do if your energy starts to drop as the day goes on.
Thyroid increases metabolism, including the breakdown of the adrenal hormone cortisol. If the adrenals are exhausted and unable to increase cortisol production to compensate, you can see the symptoms of cortisol/adrenal deficiency. This is not a problem with normal adrenal function, so if the adrenal function is low, we simply supplement that along with the thyroid.