Why do you want to use a splitter instead of connecting the aerial-out socket of the HD-FOX-T2 to the TV?
Perhaps because the HD-FOX only has one tuner and he wants to watch something on a different MUX? I think the answer to the OPs question is providing you have reasonable signal strength with the splitter in place (above 40% signal strength would be fine in my expereince, others suggest 50%) and the TV is Freeview enabled then it should be fine.