My only concern with rerouting the radiator hot water directly into PEX would be excessive water temp. Water usually coomes off the boiler in the 180-degree range, which is much to high for RFH, whether the fooring be tile or hardwood. You'd want a tempering valve to bring the water circulated in the PEX down to the 120-degree range.
I'd think the easiest and most cost-efficient retrofit would be to run the water, as is, to baseboards, and use an electric mat or resistance cable under the tile as RFH.
The baseboard will heat the room with your current heating system, and the electrical RFH will warm the tile just enough to take the edge off without causing your electric meter to spin out of control.