The main regulatory into erythrocyte production is anoxia. The response to elevated CO₂ levels in the blood (hypercapnia) is mainly to increase ventilation (i.e. more and/or deeper breaths) so that the excess can be "blown off".

I think that some carbon dioxide could pass into the bloodstream from the stomach since gases tend to be quite good at diffusing across membranes, but this would be easily dealt with by the physiological mechanism described above.

The main regulatory input into erythrocyte production is hypoxia. The response to elevated CO₂ levels in the blood (hypercapnia) is mainly to increase ventilation (i.e. more and/or deeper breaths) so that the excess can be "blown off".

I think that some carbon dioxide could pass into the bloodstream from the stomach since gases tend to be quite good at diffusing across membranes, but this would be easily dealt with by the physiological mechanism described above.