What would happen if the level of thyroxine in the blood stream could not be detected by the hypothalamus?

The person might probably die.

The principal function of thyroxine is to stimulate the consumption of  oxygen and thus the metabolism of all cells and tissues.

Thyroxine is termed T4. It travels through the blood to the target cells and becomes converted to triiodothyronine  or T3.

T3 is the active form of thyroxine. T3 enters the target cell's nucleus binding to genes responsible  or involved  in the metabolism of sugar in the body. T3 stimulates these genes and in so doing metabolism (conversion of oxygen and calories to energy) is carried out by the cell, which also results in generation of body heat.

the major parts of the digestive system:

salivary glands.

pharynx.

esophagus.

stomach.

small intestine.

large intestine.

rectum.

accessory digestive organs: liver, gallbladder, pancreas.