Yes. In terms of what is possible and what is not, there are several ways of going about this.
1, You can simply restore your device and go from a backup, which works just takes more time. About 2-3 hours total for complete setup, because you lose all you sign-ins and have to re-do those.
2, you can use an Un-Jailbreaker, and have a decent chance of being able to update, although sometimes you need a couple days for it to recognize that an update is available. keep in mind that these do not always work perfectly and has a chance of not working.
3, you can do option 1, and update your device from iTunes, as it should recognize the software, and be faster.
Hope this helps, and if you have anymore questions just ask, as I have spent a lot of time on this.
Flyer_One