The only and main problem I see is that the dip tubes in the kegs are made to be used with kegs in the vertical position. That is to say, the bottom of a corny keg is concave, and dip tubes are cut to length and angled to have their end in the lowest (vertical) part of the keg.
If the keg was exactly horizontal, about 40% of the volume would be below the dip tube at it's "lowest" extent.
You have a couple of options:
1/ Orient the kegs mostly horizontally, but at an angle, and position the bend of the dip tubes to maximize drawing. I imagine at best you'll end up having about a half-gallon of "dead space" per keg, though.
2/ Create custom dip tubes that have a more aggressive bend and a custom length to draw all the beer from the keg at a pre-defined angle incline ... perhaps even 89 degree horizontal.
(On a side note, I have to say this idea of having kegs mounted horizontally has never crossed my mind, before, but it's actually kind of clever. Pulling kegs in/out of a kegerator on their side (or, better, at say a 5 or 10-degree angle) seems like it could be a very good use of space.)