No they don't. There are several ways that the appeals process can be restarted. This is why the judge needs to be very careful in how he handles the injunctions, in order not to open the appeals process to RIM.
There was an explanation of all the various options and pitfalls written by a patent attorney, but I can't find it again. Basically it said that if the judge invalidated an existing injunction, and issues a new one that covers only the patents that haven't been dismissed, that RIM has grounds for new appeals. RIM will argue that the existing injunction, even though stayed, has to be declared invalid.
This could drag on for a very long time. It's in both party's interest to settle.