...If I turn off the adapter and the Linksys goes away does that mean the Linksys can't see me either?...
Yes and no.
Yes, if you are connecting to something...
...and getting an IP address from that something
...then that something can see/know several things about your computer. And if you have set that connection type to
Home network, then others may see shared folders/files.
No*, if you don't complete the connection...
...you don't get an IP address
...you only look at the list of SSIDs in the area.
Your wireless network adapter should not automatically connect unless you asked it to do so at some point in the past or unless the software controlling the wireless network adapter is set to auto-connect to unsecured access points.
I did not ask if the IP address associated with the wireless network adapter starts with 169. If that is the case, then it probably was not an IP from a completed connection.
*In most cases. There are tools that let people watch every wireless network adapter that is in range as the wireless network adapters look for wireless access points.