I'd think kept well covered until set up, and not left exposed too long on display, it would probably be OK............
but, that said, I wouldn't really want to have it served to me--and I'm NOT a big icing eater.
I think brides who latch onto something like this are being unfair to their guests. If the bride doesn't like icing, then she can scrape it off. Why punish the rest of the guests?
If she'll pay you for it--and sign off on something stating that she's aware that a lack of external icing coat may result in a less than optimal product if left exposed for an extended period of time AND that there will be no refunds for any complaints----then it's a VERY easy cake
Really, sometimes "different" isn't all that attractive.........and this cake is a case in point.
I'd be very tempted to add a tent card to the table that said, "Yes, it IS supposed to be this way. The baker DID NOT run out of time OR icing!"