You might notice some inconsistency with the “connect to Outlook” button in SharePoint 2013. Sometimes it seems to work, other times you may see this “control is greyed out” message below.
It's because of the effect of one of 2013’s coolest new features – the Minimal Download Strategy. You can find more about here in one of my blog here
just hit F5 & try it again. You should be able to see that the control is functional. It should temporarily allow you to work instead of waiting.