Do you have a computer with iTunes? You could back up on there and not use memory on your iPhone.
Although I’ve updated many times without backing up right before I do so, it’s always advised to backup just in case. I’ve never had a problem updating when I didn’t backup but nowadays I try to backup every time I update.
I don’t think you’d have a problem but if there’s anyway you can backup through iTunes on your computer since you don’t have enough storage on your iPhone, do it. That being said if there’s no way you can backup and you must update then I’d personally tell you that I doubt you’d have any problems. It’s just advised to do so in case something happens while updating then you would have to backup from the last time you did. If it was fairly recently (within the past week) then I wouldn’t worry about it.
When you say storage you do mean iCloud storage right? That’s where your backups are stored, not on your device itself.