No. Actually TMG is betaine, but TMG is alkalinizing although it helps produce stomach acid. Betaine HCl is acidified TMG (betaine), but it does not have all the effects of TMG.
So the next obvious question would be wouldn't our stomach acid create betaine HCl by reacting with the TMG. The answer is yes and no. First of all most people are so stomach acid deficient that most of the TMG would not be reacted with the stomach acid. And the stomach does not generate enough acid anyway to get to the acidity level of betaine HCl. Normal stomach acid has a pH around 2 to 3. Betaine HCl has a pH of 1.