Yes, because the regular season has absolutely nothing to do with the Stanley Cup, so a shortened season neither diminishes or contributes to the Cup.
That being said, I've already decided that I'm not giving the NHL any money for at least one year after the lockout ends (UNLESS I visit my brother in Durham, NC, then I would almost assuredly go to a Canes game just to see a game in a place I haven't been to), so ending it in January, 2013 merely pushes up my monetary return (not just watching TV) to January, 2014 at the earliest.
Unless you don't consider any Cup winner before 1947 legitimate... Yes.
But perhaps I should stick to a better answer, whether or not they will be true champs will depend on how I feel about the particular team that wins it.
"Trust me I'm an expert, I watched 13 rangers games on NHL center Ice this year through streaming." -Starburst
"I don't even understand what the point of all this arguing is. Are you guys hoping that the other side is going to have an epiphany and go 'Oh, OH! You're right, we ARE going to lose this series!'" -Crease