Yes, this is possible. Ive done It several times. The only thing is:
When you sync the systems, you cannot use either of them until they are done. And depending on how much you are syncing at one time, it could take a while. So set aside some time that you dont plan on playing, and do it then.
You can also transfer the games/apps etc through your computer. Works in a very similar way to the PS3 syncing. Just need to get the computer program first and it automatically installs when you plug in your vita.