You need to be rooted to even get into recovery mode, so no, you can't do that before rooting. After you get rooted, the first thing you should do is flash backup of your entire system to your SD card.
Nandroid backup will need root, simple upgrading no. You need to be rooted to get into an aftermarket recovery mode which has the nandroid backup mode. Stock recorery is done by holding volume down while powering up, You get to a little android guy triangle then push volume up and down at once, then the recovery screen. Volume down to the item you want then volume up to select it (same as enter key at this phase) THIS is what you do to install the p3 901 update after you have done the 5.5.893 one.
Aftermarket recovery's are not the same- bionic bootstrapper you tell it to restart in recovery mode and it has to be rooted PRIOR to this. Same with safestrap rooted phones only, both due to their needing to overide the stock recovery which can only be done from ROOT. Stock recovery works regardless but does not have the needed features for installing custom roms etc.. Alot of developers are talking about the safestrap though I have stuck with bionic bootstrapper and had not problems.
If stock and 901 is your goal, do the p3 method and let it take you all the way there- it still will have the ability to go back down to 5.5.893 if you want. Remember 5.5.893 is the latest official version that zergrush (the bionic root method) works on. 5.9.901 will not root unless you are already rooted and used the forever root method on the previous build... I.E. you have 5.5.893 and rooted, then forever rooted (a change to the mount_ext file, or use DHacker29's FoR3V3R root file to do it for you) After the permanent root is done then upgrade to 901 and you will maintain root.
This forum as well as rootzwiki as well as androidlife and others all have complete breakdowns with videos even on some to show you how to do this.
If you try and get stuck usually you will find you answer on one of them. If not post a question or message someone. As of late the Bionic has become sort of forgotten rom wise but it is easier to fix now and recover from failures to install properly. (wish we had the tools then we have now, maybe more rom developers would have stuck with it)
Another thought it you do root and backup you can install apps that will extract from those backups and that methods on some apps works alot better than titanium backup does for restoring. (something those of us who re-flash our phones often have to do alot
Good luck
