networking 101??

I have a simple switch with 3 connections. (A) goes to a (layer 3) Cisco switch on a 10.0.x.x network and communicates with computers connected at point (B).
Connection (C) is a direct connection to the internet 70.x.x.x.
The Cisco switch has a rule to allow it to use this connection to access the internet under certain conditions with a dedicated IP address. The Cisco switch does NOT normally use this connection.
Question: under normal conditions can the internet connect to computers on the 10.0.x.x network via point (B)?