Heater Core Lines

[vex]

Is it mandatory to connect the heater inlet line to the radiator?

Here's my situation: I have an aftermarket radiator, but no T-fitting that can mate the line from the firewall back to the radiator and water pump inlet (at least from what I have found. If some one knows of a simple fix for that then I'm all ears). I'm currently running a T-fitting from the heater inlet on the fire wall to the turbo, and a T-fitting on the return line from the fire wall to the turbo.

I'm thinking that I will need to run the line from the heater inlet to the radiator so that cold coolant can be circulated directly into the heater and turbo. Is that thinking accurate? Could I get away with no hooking up that line and not running it to the radiator? The coolant temperature would get warmer, but would not be excessively hotter than normal I wouldn't think.

Suggestions?