The short answer is: yes. Progressive web apps do work on devices running on iOS. However, there are a few limitations when compared to browsers like Microsoft Edge or Google Chrome.
It's important to understand that these limitations are largely overblown. Progressive web apps are just as great a bet on iOS as they are on android.
One of the shortcomings of Safari, for example, is that even though it does support the use of service workers, it does not allow for push notifications.
Unlike Chrome and Edge, the Safari browser does not support a native add to home screen cue.
All that aside, a PWA still offers a native app performance within the browser. You still get a web application that does not need to be downloaded, works on offline devices, and can be accessed anytime and anywhere.
All in all, it seems like having a progressive web app is worth it no matter the operating system. Other platforms may have been more supportive of the PWA development than iOS, however, it isn't as big of a deal as it might seem.
Conglomerates like Twitter and Alibaba continue to see massive conversion increases both on android and iOS, proving over and over that progressive web apps are a great addition to native apps.
Furthermore, as slowly as they may, Apple does continue its progressive web app development, presenting new functionalities over time.
Should you get a PWA for iOS then? If you're looking to improve your conversions and sales there is no real reason not to invest in a progressive web app for iOS.