@mar1kle

Not much glycine is lost with usual aspirin doses (30% or less of the aspirin weight).

The amount of sodium eliminated in pairing with salicylate ions should also be low. Approximations:

Aspirin

1 mmol per 180 mg (from 180 g/mol⇈) 5.5 mmol per 1000 mg

Sodium

5.5 mmol of sodium is 130 mg (from: 5.5 mmol × 23 mg/mmol)

Maximum direct sodium loss:

130 mg Na/g aspirin

It may seem negligible, but it depends on the amount consumed of each.

Global, regional and national sodium intakes in 1990 and 2010: a systematic analysis of 24 h urinary sodium excretion and dietary surveys worldwide

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For a person ingesting an average amount of sodium (4 g), taking high doses of aspirin can induce the depletion of a considerable share of the sodium intake.

As for the alkalinization, it may enhance the activity of acyl-CoA synthetases (ACS), mentioned above as the limiting step, similar to the disinhibition effect on some glycolysis enzymes.