I've run my water cooled turbo without the water cooling lines hooked up in the past. Also have run oil cooled turbos in the past on my volvo and have had to block the water lines off You can run it, and it will last, but your idle down time will become ESSENTIAL! Also, do not forget to let the turbo warm up before you go for a drive. While it is doable, its just not too smart.

Just do the right thing and tee off your heater hose like everyone else is saying. If it is closer to your expansion tank, you can tee that off as well (thats how my volvo is setup). The few extra minutes or hours that it takes to tee the hose will save you much time in the longrun spent idling your car down, to go run into a store etc.

Not to mention, if you neglect the idling procedure, especially on a turbo sans watercooled bearings, you WILL (not can) cook the bearings. Its just safer.