Yes Icon, this doesn't happen as probably intended.
If you accept an invite from the Game Client, the transition is far smoother.
More often than not , if you don't have your game client window open and simply accept an invite from a page within WGT site, it takes far too long for the accepted invite to register to the host. Sometimes the game client doesn't open at all.
This is why when I go Green - available, i will always open my Game Client as well. So as to not miss invites due to this.