[geezer#99]

The yellow arrow points to the hot air tube. It’s function is to supply hot air off the manifold. You need heated air during the warm up time when you first start your motor.
The vac hose to the green arrow is a manifold vac source. The vacuum pulls a flapper door shut in the air cleaner snout. Once the motor starts to heat up, there’s a coil inside that cap that overcomes the vacuum and the flapper opens to let fresh air into the snout.
Your headers will eliminate the hot air tube. The air cleaner flapper will always stay shut ( no heat to heat the coil) and the only air to your carb will be thru that small hole when you remove the heat tube.
You can run it with headers and a different air cleaner but you could have first start(cold) problems until the intake warms up.
If you’re creative you can remove the shroud on the manifold and adapt it to headers and keep your air cleaner working like normal.