Can I restore items from a Mavericks Time Machine after upgrading to Yosemite?
There's no reason why you shouldn't be able to recover files from a Time Machine backup saved using Time Machine under Mavericks simply because you upgraded the Mavericks system to Yosemite. A system upgrade doesn't normally break continuity of Time Machine. There will likely be a lot more data backed up during the first backup after the upgrade, so if you don't have enough disk space for the new backup data, some older backup data might be removed to make room for it.

As long as you have credentials to access the backups, you can recover from your current Time Machine backup from another Mac that has been configured for Time Machine whether it was upgraded to Yosemite or whether Yosemite was originally or cleanly installed. Just connect your Time Machine backup to the computer you want to use to recover, hold down option, then click the Time Machine menu and choose "Browse Other Backu Disks...".