I've thought about this but did think it would probably have beer / hops aroma in the water, I can smell the beer ferment in the house during any ferment.
You would also need to get the water very cold if it was at room temp of 20 celsius and 12 psi you'd only get about 1.55 vols of CO2 in. If you chill the water to 4 celsius the vols absorbed would be about 2.6.
I normally have more than 3 vols in my sparkling water so you'd need to up the ferment pressure to 35 psi at 20 celsius or 18 psi at 4 celsius.
I suppose an inline carbon filter might scrub the aromas before the keg is a possibilty.