Update Permalink Structure = All Links Automatically Update?

Generally, yes. All your links will be automatically changed and they will work normally.

Krishna, thank you. There is no danger, or little danger, of anything becoming messed up?

No chance?

I don’t find any problems while changing permalinks. If you are apprehensive of any problems, you may backup your site first and then change permalinks so that you can restore to what you have now in your site.
Also review: https://codex.www.ads-software.com/Using_Permalinks