TLDR: @Craig has a better answer above.

Below is my original answer, but I do not believe it answers the question adequately. Today I would say you'd have to try a library to emulate this effect, as A2HS is not supported in WebViews (PWAs).

@Kerrick I would like to delete my answer, but cannot as it has been accepted.

Old answer:

Yes. The majority of modern browsers support the Add to Home screen (or A2HS) feature for Progressive Web Apps. To quote the Mozilla Web Docs article:

Add to Home screen is a feature available in
modern browsers that allows a user to "install" a web app, ie. add a
shortcut to their Home screen.

See also: A2HS browser support at caniuse.com