Yes, it would produce some CO2, but not enough to make a difference.
You need to significantly raise the CO2 concentration and maintain it, which is a bugger cos you also need to ventilate the space for heat, but the advantage is you don't need to worry too much about venting for CO2. An effective setup needs air cooled enclosed lights so room temps are minimised, lower room ventilation right down, and use a proper CO2 setup that maintains a set ppm. It is expensive, tricky to get right, and if it goes wrong it can kill you with no warning. DIY is not recommended.
If you have a large (commercial) setup then the payback may make sense - they use them more and more in commercial glass Houses, especially if the CO2 can come from a commercial generator or other source where it counts as carbon capture.
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