Right but then you don't have any hope of having something resembling the quark model. I agree that you can make a color singlet state out of the fundamental of SU(2) of course.I don't agree.
Both meson states and diquark = baryon states of SU(2) color are constructed as 2 * 2 = 1 + 3 where '1' is (for both mesons and baryons!) the physical color singulet. Using 3 * 3 would correspond to quarks in the adjoint rep. of SU(2) color which is of course something totally different and does by no means correspond to QCD.
Another issue for SU(2)c is that again b/c of the pseudo reality of the representation, the mass generation mechanism for the quarks is going to be quite unlike the real world as it is not a chiral representation and the HIggs mechanism doesn't necessarily work.
I'd have to think about it, as its somewhat subtle but I think there will be some sort of mass generation for the quarks arising from chiral symmetry breaking. Its a little upside down from the usual process (normally chiral symmetry is broken by the quark masses).