Hear me out. This thought process requires a bit of knowledge of physics/chemistry.
On the martian poles, there are vast quantities of frozes CO2. This frozen CO2 exerts a certain “vapor pressure” - in other words, a certain partial pressure of gaseous CO2.
Now, if we convert this CO2 into O2 by removing the carbon out of it, the concentration of O2 in the atmosphere increases. And therefore, the concentration (and partial pressure) of CO2 decreases.
But since the frozen CO2 on the poles causes a certain partial pressure of CO2, a bit of the frozen CO2 will go into gaseous phase to refill the CO2 partial pressure.
So, by converting CO2 into O2, the concentration of O2 increases, but the concentration of CO2 stays approximately the same. As such, the total pressure (and density) of the atmosphere increases. This would happen if large-scale biological photosynthesis/growth took place.
Any thoughts?
Unless you can generate a magnetic field around the planet sufficiently powerful enough to prevent solar radiation from blasting the atmosphere away, it wouldn’t change anything.
Mars needs a molten iron core or something like it to be terraformed for any meaningful length of time.