The pause can be considered normal, although it's a bit long, but might be if your system is taxed with many addons.
What shouldn't simply happen (and no tester has ever reported this), is the loss of focus, the GSX Window is a standard Simconnect window that is created using the official SDK method, so it's controlled entirely by FSX itself, with regard to window creation, focus handling, messaging and all the quirks that might happen if you create windows yourself in the code, which is not what GSX does.
Instead, it's likely you have another addon that is "stealing" focus *from* FSX.
UNLESS you are using Prepar3D, because the loss of focus is a very well known Prepar3D bug, that has been already raised ( by myself, but not only...) on the LM forum:
http://www.prepar3d.com/forum-5/?mingleforumaction=viewtopic&t=484http://www.prepar3d.com/forum-5/?mingleforumaction=viewtopic&t=448It affects even the default ATC in P3D, hopefully they'll fix it.