I'm pretty sure you can. I was able to with ML anyway. I don't think it changed with maverick. I had some issues with access denied for some dates though. I'm not sure why though.
Yes you can. A Time Machine backup to a local disk since lion 10.7.2 has a recovery partition on the backup disk. So you just option key boot to the time machine disk and use disk utility to erase your disk then click restore. That will place the OS and all your data back on the disk.