Glycerol itself is a component in the triglyceride molecule in triester form. That is why triglycerides are called triacylglycerol. Actually triglyceride is a misnomer. So as without the glycerol moiety, there cannot be a triglyceride and there is no question for glycerol-correction in triglyceride or triacylglycerol correction.
Yes, you are correct. In experimental studies, as well as in critical clinical diagnostic and management situations, glycerol correction will definitely improve interpretation.
The SIGMA Serum Triglyceride Determination Kit Catalog Number TR0100 is applicable for accuracy level sufficient for clinical use. For extra ordinary accuracy and reliability under specialized experimental and/or research condition, the same may be used with modification of the calculations considering the molar concentrations of glycerol and normalized serum triglyceride profile. The kit literature is attached.
I suggest to analyse free glycerol before transesterificaton of tryglicerides and after transesterification as reported in a paper published in Food Chemistry:
Rapid determination of esterified glycerol and glycerides in triglyceride fats and oils by means of periodate method after transesterification.
In this way you have the possibility to determine free glycerol in a very specific way and after transesterification you can analyse the glycerol contained in tryglicerides. This is a very good method of analysis!