Yes, but the best way to enjoy your Bandcamp purchases on iOS is with the Bandcamp app!
Create a free fan account.
Install the Bandcamp iOS app.
Stream and enjoy your music instantly. (Supports Chromecast and Apple CarPlay, too!)
Download for offline listening in the app.
If you’d like the audio files saved on your iOS device, follow these steps:
Tap “Download your purchase” in your email receipt.
Your files will download as a .zip file.
Open the Files app and extract (unzip) the folder.
Open a music player app that supports local files (other than Apple’s Music app) and enjoy.
Important: This method does not allow you to load your downloads directly to Apple’s Music app due to limitations imposed by Apple. If you want your purchases in that app, you must first download them to a computer (any format is fine) and then sync them to your iOS device.