If you add CA certificates for the Wifi they probably (I'm not sure if you can tell it manually to not do that) are added to the system-wide trust store. IE and Chrome check that for CAs, Firefox will soon (https://bugzilla.mozilla.org/show_bug.cgi?id=1265113)
(all this for Windows, I believe the same is true for OS X, Linux depends on your specific your setup)
(all this for Windows, I believe the same is true for OS X, Linux depends on your specific your setup)