TETB is absolutely right (How could he be anything else
)... it is an interesting question though if not using a non return manifold. You'd need to consider vapour pressure and diffusion rates when not using your system, since as soon as you pour a pint the gas in the line will be replaced fresh. If you consider the volume of the tubing, a pressure of perhaps 10psi, and dry bulb temperature of a kegerator at maybe 10°C. Let's assume your vapour from your kegs has reached equilibrium in the pipes.
In a closed keg at equilibrium the relative humidity is always 100%. The liquid evaporates until the partial pressure of the vapour reaches the maximum value for the temperature. So that allows calculation of the absolute humidity for 10psi 10°C at 0.00579 kg/kg. the volume of gas in a line is V = πr^2h. Let's assume you are using 3/8 gas line with an internal diameter of 6.7mm, and the length of tubing from cylinder to each keg is perhaps 2m. So your tubing is volume is going to be 0.00056 m
3, or at this pressure 0.01652068 mol of gas. For CO2 with a molar mass of 44.01 so the mass of gas in the tubing is 0.41mg. Your mass of vapour is thus going to be 2.3 µg - which will comprise a mix of both vapours. ie not a lot.
There are some complexities here as there will be some diffusion over time between the two kegs, and while this would be slow, it could mean that a vapour component could eventually, very slowly reach equilibrium in the other keg headspace - this will take a very long time though since both kegs are sealed and at max relative humidity so you're relying on simple diffusion in a still gas. There's also odd things like the pressure drop in one keg while the other is being served that will to a tiny degree suck the vapour from one keg into the other. The masses though as you'll see above are absolutely teeny weeny.