Can I use Add to home screen in Chrome on an iOS device?

No. There is no such option in Chrome for iOS. I'm using iOS 12 on iPhone X with latest Chrome and I don't see such option. Safari for iOS have "Add to home screen" for a long time now. Its just the "Service worker" support that came recently in 11.3 version .

Notably, Chrome for iOS is just an wrapping layer on top of Safari's WebKit and what it can perform at OS level is heavily restricted in that sense. Depending on when and how Apple opens its API for 3rd party WebKit based browser implementer for iOS, we can hope to see this sometime in future.

But still not an option for now (as of May 2022)

Actually there is an application ”Shortcuts”, it can run any action on your iPhone or iPad. You can create app shortcut. It works with Chrome.

Here is the app link

https://apps.apple.com/ru/app/shortcuts/id1462947752?l=en