I browsed around your site, it seems that many pages, hit or miss, have very high load times. Connections will only affect the page on which the
[connections] shortcode was added.
I see you have at least cMap and Form. I can tell from the minified CSS and JS. I found the page with Form, but not cMap. Can you please share a direct link to that page?
As for the load time for the Connections page, how many entries do you have on it? I recommend no more than the 20 that cMap defaults to as a max. WordPress limits posts per page to 10, one blog pages, in order to help prevent long load times. Having to many posts or Connections entries on a single page will cause many database queries. So this really is not a issue limited to Connections.
I also see that you are using W3TC, great plugin, I use it too on this site. One thing to keep in mind, it can create very high server loads when not properly configured for your webhost. I highly recommend turning off most options and enabling them one at a time doing after doing page load time analysis to determine if the feature is providing a benefit or not.
I hope that helps!