Can one reduce solubility of NaCl by adding CO2 under pressure? Will the salt fall out of solution?
NaCl is vastly more soluble than carbon dioxide, so this method won't work.  You can get some NaCl to precipitate (assuming you have a concentrated solution) by bubbling HCl in, thanks to the common-ion effect, so you could for example get pure NaCl from rock salt this way.  But somehow I don't think that's the situation you have in mind :-)