It probably wouldn't speed up the process. First, just because some company implemented 1-click, does not force Amazon to sue. Unlike trademarks, where the mark has to be enforced to prevent delusion, patent infringement can be ignored. RedHat has even gone so far as to publicly state they won't enforce their patents in certain situations.
Second, even if it was brought to court, the judge could decide to stay the case pending the decision from the USPTO. This sometimes happens because the judge doesn't want to waste their time or effort when the USPTO is already looking at the case.