I've seen this done.
Pro audio cabinets aren't made from MDF, however.
The ones that are surely aren't touring worthy!
A lot of the carpeted "baltic birch" cabs are quite rough underneath and the coating isn't going to hide this. All in all it should still look better than jacked carpeting. The option is available with manufacturers from the factory at a price premium as there is more labor in prep to get them looking acceptable.
I've seen some pretty ragged Peavey cabs in the Caribbean and they're still kicking out the tunes.