I have a 2007 V70 2.4L that I recently bought. The silver pipe in the photo was broken so temporarily duct taped it but curious what the pipe is for?

 

That flex pipe connects the heat stove around the heat shield on the exhaust manifold to the air intake box. Its purpose is to have warm air enter the engine on cold days. There is a thermostatically controlled valve in the air box to regulate the temperature.

Wrapping it like you did will work just fine.