Yes the model can just sign a 'universal' release. I have been using the istock release and everyone excepts it except dreamstime. The istock release however doesn't have the words istock in any of the words so it is easy to just crop out the istock part of the release and then dreamstime is ok with it.
As per uploading the releases. It totally depends on the site
Fotolia, Feature Pics, 123RF, and StockXpert all store the releases on file, and thus you just have to 'point' to it.
The other sites, like dreamstime, shutterstock, and istock and the rest you have to upload it seperatly for each site. It isn't THAT much work as the release file is generally pretty small (as small as you can make it while keeping it legable).