CO2 isn't a solvent.
If you are thinking of "CO2 extraction" by supercritical phase transition using CO2 under huge pressure, it's the phase change and not the CO2 that acts like a solvent. So, no it won't help improve your tincture..
Best case scenario: You waste a sodastream charger and wonder why the experiment?... or
Worst case scenario: You blow a mass amount of pressurized flammable alcohol spray (picture a gasoline shower) and hash oil that blinds you and starts a fire when you aren't watching. No shut off valve either if a seal fails. Are the seals in your sodastream alcohol proof? Sometimes "tried and true" is the best path. I do love the idea that you are thinking "out of the box". Just please be safe.
Alcohol spray isn't just flammable, if you get the right air/fuel mix, it explodes with the force of TNT.
Plus the neighbors just get pissed when the fire department asks for some marshmallows.
Where my primary home is in California, the local paper posts pics of exploded and burnt down houses EVERY week.
All from solvents and hash making.
Think about it...
Best,
FM