the upgrades are rather seamless, and how i recommend doing the upgrade would be to choose a time of the lowest traffic based on your analytic stats. i can assure you that its more of a PITA trying to do it locally then pushing it up on the server. the process for these updates is fairly simple, you upload the zip file to the server, unpack the zip file and it overwrites the files, then you run the upgrade script. if you have not hacked core files all should go well. then there are a few adjustments at the end of the upgrade script that tells you exactly what you need to do, chmod some files and remove other files. I upgraded a 6.1.6 to 7.0.5, and all went well.
running the upgrades locally then attempting to push up the files via ftp opens the door for other great Darwin anomolies, and whereas your intent is to not have downtime on your site, maintenance on a site is inevitable, as long as you send out notifications, and all of your members are aware, and you load a maintenance page, there is really no harm in being down a couple of hours.
the key to this all is backing up each version as you upgrade, and not only the file structure, but also the database. dont take anything forgranted, and always expect the worse and be prepared, and that would be the synopsis on whatever approach you take on upgrading.
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