If there is only specific section you'd like to share (connectionStrings in your case) then linking wouldn't work for you. Instead you could do something like this:
The solution is to store the connection strings on the web.config of the parent web app.
Note that the web site root is also an app, so you can store a web.config in there (i.e. c:\inetpub\wwwroot\web.config) which will be inherited by all apps under it.
c:\inetpub\wwwroot\web.config -> common configuration.
c:\inetpub\wwwroot\app1\web.config -> configuration for app1
c:\inetpub\wwwroot\app2\web.config -> configuration for app2.
In the case the default web site root is off limits, you can create a root app to contain all other apps and store the common configuration there.
c:\inetpub\wwwroot\myrootapp\web.config-> common configuration. c:\inetpub\wwwroot\myrootapp\app1\web.config -> configuration for app1 c:\inetpub\wwwroot\myrootapp\app2\web.config -> configuration for app2.