I did it with a fixed gear Centurian Accordo roadbike. I just had 3 stem bar combos (northroads, bullhorns, drops) to swap in and out. Most bikes of that vintage have adequate tire clearance to put decent size tires. I used cross tires on mine and had plenty of room to spare. I took this offroad, on road, on ice..... Fine in all ways with all bars. Other have chimed in about size and brake aspects already.
Go for it. It is a good way to get a 'new' feel from an old friend. There is no reason not be be comfortable. I would think about anothe seat (personal preference though).
Note - if you want to convert it very inexpensively, you can find an old 3 speed or or single speed cruiser with handbrakes and 'swap out the bars'. (I found one at a neighbors garage sale and took the bars and brakes and stem. For $5 I had another option for my bike.