Is it save to backup and restore from iTunes?

I'm using an iPhone 4S and I have been using it since Oct 2012 so it hasn't been a year I use the phone. But it seems like I'm experiencing a problem after I updated it to iOS 7 just yesterday. Every time I open an app a pop-up show: "connect to iTunes to use push notifications" and I've googled for the solution, but I haven't find one that is satisfying. Ppl write that I should back up my data to iTunes or iCloud and restore it again. I'm afraid that restoring my data from iTunes won't fully restore all of my data. So for those who have done this before, is it save to backup and restore data from iTunes?

And if you have any other solution for that annoying "connect to iTunes to use push notifications" popup beside backup-restoring and redsn0w, please tell me.

One way to back up your iTunes library is to consolidate your library into one folder and then copy that folder to an external hard drive. This is a painless process that only takes a few moments to accomplish.