Not really. But after nought, it is always recommended to keep android system web view up-to-date. Although, if you don’t want to, it wouldn’t be any issues at all.
Android system web view is like a browser. Actually, it is a browser. When you open some links from other apps, on older versions of Android, it used to give you an option to select a browser to open the link. You might have noticed that now a days, if you click on a link from some apps, it immediately opens without asking you to open from a browser. You are initially opening the link from android system web view. as of my experience, I never updated that shit in my life before 2-3 month. Used a year old version without any issues. On my old device.