Unless I’m missing something, you can’t add a portrait to a hidden character. It tells you the character doesn’t exist. You have to make the character visible for long enough to give it a portrait and then hide it again. I suppose your players won’t be monitoring the game every minute, but you can do everything else while they’re hidden (if only by using the GM Menu) so why not portraits?

If it’s not possible to code for browsing, is it possible to insert the portrait reference number while the character is hidden? You could then browse portraits from a visible character and just insert the chosen number in the hidden one.