You are talking about the Air Injection System.
It supplies air to the exhaust ports to help combustion of unburnt exhaust.
And yes you can run with out it...my 86 4Runner 22re has no AIS.
FWIW- It is not part of the EGR system.

Anyway, I have a good exhaust manifold I would not mind getting rid of.(I mean, my wife would like me to throw out).

1991 FJ 80 Land Cruiser for fun.
1998 GS300 for the wife
1998 GS400 for me
1991 Supra SOLD
1986 4Runner 335k miles-22re EB inside.SOLD