Possible, but likely expensive. See https://www.researchgate.net/post/What_is_the_cheapest_13C-carbon-source_available

The problem using 13C is that there is a natural abundance of 13C of 1.10% of carbon atoms. Consequently, one has to use food containing considerable quantities of 13C to overwhelm this background. It is by far easier to use 14C, which although it exists in background as it is (believe it or not) created in the upper atmosphere by cosmic ray spallation. Carbon-14 occurs in trace amounts, i.e., making up about 1 or 1.5 atoms per 1012 atoms of the carbon in the atmosphere. The half-life of carbon-14 is 5,730±40 years.

For example, both 13C and 14C detection methods exist for helicobacter pylori detection using 13C or 14C labeled urea, but the 14C method has better ability to detect or exclude the bacterial overgrowth in the stomach and proximal gut. And, that is a special case, since the digested urea is promptly exhaled after turning into isotopically labeled CO2 so that the labeled urea is either digested by the bacteria and promptly exhaled, or excreted unchanged in urine .For the urea breath test, one has only to give a small amount of labeled urea, because normally it is not turned into CO2 at all.

The problem becomes harder when one gives food that is normally used to make muscle, for example. Then our background is much higher, as we are not looking at the mass of CO2 produced in the body over 2-minutes, but at a percentage of normal tissue isotopic abundance, far greater masses, and much longer time periods, and the amount of 13C needed in the diet would probably be cost prohibitive. I would suggest using 14C beta detection instead.