I can't see any reason why they wouldn't. I picked up a growler of stout from my favorite brew pub on Friday. I haven't ever gotten a growler that lasted for more than 24 hours so I can't answer how long they stay carbed. They sell them in the liquor stores out this way so I can't imagine they go flat that quick.
Cask beer isn't carbonated. The foam an engine creates is due to air being pumped into it. If they can fill your growler bypassing the engine, then great. Otherwise there will be too much oxygen in the beer.