Absolutely! I have had early 1950 models in .30-06 and 6.5x54mm MS. The Mannlicher Schoenauer MCA was made in .308 and .243, but the .308 Win is hard to find.Mannlicher Schoenauer (made in 1906 I think) with the open vee & folding peep rear sight is on my wish list - Absolute class!
I doubt you would find one in 308 though. I shot a beautiful 7x57 example at 300 yards a couple of years ago & hit the bull first shot. Fell in love on the spot!
The older Steyr Mannlicher Luxus (not the take down one) comes a very close second. - I have one in 30-06 .Unfortunately it comes with just the barrel mounted open vee sight & not the rear peep.