[AXMonster]

It would work a little, but the gains would be small as heat rejection through the manifold is small compared to the total energy of the exhaust gas.

Also it would be risky if maximum pre-turbine temperatures exceeded the maximum limits (typically atound 720°C for non-water cooled small passenger car turbos) when towing or driving hard for example.
But if you never drive hard or tow up mountains etc then you should be safe.

It all adds up, and with a modern VNT turbo the small gains in energy driving the turbine wheel may well result in lower pre-turbine pressure as the vanes would be open more for the same boost. This would have a knock on effect with lower pumping losses.