Okay...I deleted my first response because it seems that I mis-read part of the first post. Let me try that again...
Contrary to what most people think, it is NOT illegal for a fielder to block a base without the ball. A fielder can stand anywhere on the field she pleases.
Now, before anyone thinks I've totally lost it...let me explain. If the fielder does not have the ball, it is illegal for her to block the base AND impede the runner's progress. Obstruction requires BOTH elements before it can be called.
For instance...if the catcher is in the basepath, blocking the plate, that in itself is not automatically obstruction. It's entirely possible for the runner to come in and never break stride, change her path, slow down or contact the catcher. In this case, the runner has NOT been hindered or impeded and it's NOT obstruction.
It can be a fine line and a grey area to judge and the final determination is up to the umpire's judgment.
Plugging all that into the original question...did the runner have to slow down, check up, go around or otherwise alter her path to the plate BEFORE the catcher secured the ball? If so, then obstruction would be the right call. Award the runner home.
On the other hand, if the runner did not alter her path in any way, then by definition she wasn't obstructed. This would be a legal tag of the runner and she would be out.
From a practical standpoint, simply blocking a base without the ball is not illegal. Blocking the base AND actually impeding the runner is. Whenever a fielder blocks a base without the ball, it opens up the possibility that there will be an obstruction call, but it isn't automatic.