Don't even try to run it that way, you will destroy the bearing races. You want to get the right side cone and lock nut set firs. Then get the left side set right, tighten the cone nut till you feel drag when you spin the wheel. Then back it out a lil bit till it freely spins again. To finish up, grab the coaster brake lever and cone wrench with one hand, and tighten down the lock nut with the other, making sure the cone doesn't spin on the axle at all as you tighten it down.
On another note, it looks like you have caged bearings. Go to the bike shop with a ring and buy double the bearings in the cage minus 2, empty the bearings out of the cages and put half on each side. I've never had a caged bearing last. The cage always gets mangled on a bump, then its a fun time getting home.