You can paint over chrome, it is not particularly durable.
My Atala with chromovelato head tube is House of Color candy red directly over chrome.

I can't speak for the bike you reference, but plenty of other bikes began life with paint over chrome. I had a 60's era Falcon, for instance, and a 1984 Centurion Turbo - both of them had paint covering a fully chromed frame. I had a Bottecchia with all but the top tube chromed under the paint (and that was a weird discovery.) Those examples alone represent Britain, Japan, and Italy. Typically, those chromed frames were not polished under the paint - only where the shiny stuff was intended to be seen was it polished. And while I wouldn't describe the paint on any of those three to be nearly as permanent as, say, those stove pipe black tubes of an early Raleigh, neither was it peeling off. I guess what I'm saying is that you can definitely paint over chrome, and as GB has already pointed out, the chrome on chrome lugs doesn't just stop where the paint begins: it's at least partially under the paint.

But if you're going to have your bike painted, be sure to have this conversation with the place doing the painting. If it's a place like Waterford, for instance, they will have experience painting over such stuff and will tell you how the frame needs to be prepared.