I'm not entirely sure what you're trying to do here, but here's a few things I notice off the bat:
No, the PanelGrid isn't going to be refreshed by the inputText - because there isn't a render="teamsGrid". But it will be rendered if the button is clicked - except that then the inputText won't be executed - except that it got executed via the blur first.
So, it should work, but it's a shaky foundation that I wouldn't recommend. Why use the blur at all? Leaving that off is probably going to make better code.
And, lastly, I've generally steered clear of c:forEach, because then I don't have to worry about this:
http://www.ilikespam.com/blog/c:foreach-vs-ui:repeat-in-facelets
But prehaps your problem is somewhere else entirely, it's hard to tell.
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