Even though that "might be" the main purpose of that line, it is also for other things. It also helps eliminate any air from the system. If it becomes plugged, air elimination is hampered.The 1998-2002 LS1 Camaro/Firebirds have a simple, non-pressurized over-flow tank. The only connection to the over-flow tank is the line to the radiator filler neck, just under the cap. There is a throttle body connection (1/8" tube into hose) that runs to the top of the radiator just under the filler neck. I have seen that TB entry hole exposed a couple times now. From what I have read "GM ran the upper engine steam line through the TB in order to heat the TB to prevent icing in extremely cold weather but mostly to aid in cold start warm-up. (less cold-start emissions and faster warm-up times." I will make a note to check that line for flow into the radiator next time the level is down 1/2" or so.
The real issue at hand is that it may become plugged with chunks of rubber hose internals, or other gunk like Bar's Leak, which was sometimes added at the factory. (in those days).
The important thing to remember is NOT to blow it back into the block IF you find it plugged. That will just keep the problem for another future time.
Remove the hose and check where it comes from, remove any debris, and reinstall.
Think about it, it doesn't have a seperate thermostat or control of any kind. It needs to flow ALL the time.