I don't think he is joking, as he was a jobbing actor/musician for years and years, doing loads of little voiceover stints and guest vocals here and there. And if he's taking the mick he and his musician pals must be very committed to this specific bit. (Plus, it's in his Wiki entry, and their source is a What We Do In The Shadows Youtube interview featuring him, so straight from the horses mouth)
God I would love Matt Berry on Strictly, but each week as a different character ( Lucien Sanchez , Steven Toast, Douglas Reynholm, Laszlo Cravensworth) and nobody points out anything odd about it. I think Claudia would love it, I can just see her playing along as "Lazlo" tries to seduce her.