iTunes Internet Radio on iOS
Yes, it is possible but requires a bit of copy/paste work.


Select the radio stream in iTunes on desktop.
Select the Edit menu, choose the Song Info entry (or just press Command + I). This will show you the location URL of the stream.  For example, the first stream in the 80s Flashback section is A_A 80s with the URL of http://listen.shoutcast.com/a-a80svs90s.
Click the URL and it will select all of the text.
Copy the URL to the clipboard (Command + C)
If you have your desktop setup to use Handoff to your iPhone, open the Web browser on the phone (Safari and Chrome both work) and paste in the URL. The page will become a simple media playback bar.
If you don't use Handoff, open the Web browser on your desktop, open the bookmark manager, create a new bookmark with the URL of the stream. Hopefully you have your devices configured to sync your browser bookmarks, if so, the stream bookmark will appear in the iPhone browser.
Finally if you don't have the devices configured for sync, you can copy/paste the stream URLs into a new email message on your desktop and then send it to yourself. Open the email on your phone and click on the stream URL, which should load up in your Web browser.


As nohillside mentioned above, it might be easier to manage the streams using an Internet Radio app from the AppStore. You should be able to add the stream URLs from iTunes into any Radio app.