The original wheelset on my 1960s Cinelli was 5-speed one side, fixed the other. I always ran it on the 5-speed freewheel, and kept it that way when I had to buy a new rear wheel (the 42t small chainring gives me enough problems on steep hills as it is!).
Chain line is difficult. My fixed gear bike has what looks to me like a really good chain line, yet it's thrown the chain when leaning into corners over bumpy ground a few times now. If you think it could be improved upon, I'd try and do it, you don't want to have an avoidable accident if the chain unships and jams in the rear wheel.