It will not have high enough quality, I'm sad to say.
If you keep the sRGB gamut, it takes about 12 bits of linear precision per component to still generate every 8-bit sRGB value. Of course, the problem is most severe at the darkest of shades, but it doesn't really change things too much to just go full 3x16 or 4x16 bits compared to some more limited solution.
For the remoting protocol, it is thinkable that the fidelity of the rendering would be reduced during the process, but the focus should be very strongly on getting good local behavior and treating the remote behavior as afterthought. It's probably not so hard as people think, and in any case we must not cripple local features for sake of preserving remoting, imho.