Pressure, Physics, and CO2

I've been mulling a CO2 delivery method that *doesn't* involve bubbles in the tankwater, for purely aesthetic reasons, and would like to ask a couple of questions before I proceed. It seems to me that if there were a way to temporarily pressurize the CO2 and water together, then the CO2 would enter into solution, much like a coke. (Yes, it will come out of solution after the pressure is off, but maybe it will last long enough.)

So, I've come up with adding a tee fitting in a horizontal portion of the 1/2" PVC return line of my external Little Giant pump, with the tee pointed straight up and connected to a length of 1/2" PVC vertical pipe. At the top of that vertical pipe would be the CO2 input connection.

Then the CO2 would be introduced at a rate that pushes the water down, resisting the water pressure from the pump but not so much that the CO2 enters the water flow directly, and hopefully pressurizing that vetical length of pipe to the point that the CO2 would enter the water in solution. I might use a piece of clear PVC for that vertical pipe so I can see the height of the water column inside.

Does this have any possibility of working? And, is there a way to calculate how long that vertical pipe should be in order to build up enough pressure? I can do two feet easily and keep it concealed, more would be harder but worth doing if the concept might work.

Thanks,

TW