No, it does not avert a Government Shutdown. Here is what this blog post from the Washington Post says:
Democrats on the House Appropriations Committee tell me that they are worried about the possibility of major sticking points looming over so-called “policy riders,” a threat that still remains even though Congress has agreed upon new spending levels that are higher than the caps imposed by the Budget Control Act, a.k.a. the sequester.
The problem is that, even though the bulk amount of spending has been agreed upon, Congress will have to pass a dozen or so individual appropriations bills that fill in the specific spending in different areas of government. Democrats note that half a dozen of these bills have already passed the House, and all 12 are public. They’ll have to be renegotiated to align with the new, higher spending levels.
But the already existing bills are currently loaded with policy riders on all sorts of conservative priorities, Democrats point out. Conservatives will likely pressure GOP leaders to keep these riders in, and pressure them to make them conditional on passing these bills — creating another leverage point that the right can try to exploit, potentially leading to sticking points that threaten government shutdowns.
So to sum up, appropriations haven't been done yet, and Republicans are currently putting policy riders in appropriations bill, so there's still a possibility of a Government Shutdown.
And given that Paul Ryan has just been elected as Speaker of the House promising to "take the fight to the Democrats", and Tea Party members are already angry at the GOP leadership about the budget deal, I think there's a significant chance that of a Shutdown threat.