I just complete rebuilding my fuel system on ody 350.

I started it up without putting the air box back on just to make sure it would start. I ran it for a couple minutes and then noticed fuel dripping on the floor. It appears to be coming out the large air intake on the carb that attaches to the airbox.

Is this normal? Or does it indicate an issue?

Dripping fuel is not normal. Float valve should shut off fuel flow when the bowl is full. I would check the float level.

Yes you will need to take apart again and check your float system.
Make sure the floats are set to correct height,and are not leaking too.
Whenever I have finished servicing a carb,and BEFORE installing the bowl,I attach a clean line to the fuel inlet spigot and mouth blow while inverting the carb slightly to activate/see where the float shuts off.You will feel your blow get harder and harder,get chipmonk cheeks,then stop if all is working OK.Then I suck hard and if my tongue vacuum sticks to the tube,then all is OK too.
This way you can verify that the whole float system IS actually working properly BEFORE installing by simply simulating the fuel shutoff just by the line/mouth blow check method.
Warning petrol tastes horrible...plah,spit spit!

Well. Found the issue. My fault too. I was showing my son how to put it back together. And he put the float valve upside down. He asked me if it was correct and I didn't look closely enough. I can't believe it started at all like that.

Glad you found the problem. Hopefully the bottom end is not loaded up. May run rich for a while until it clears up.

I don't think so. The carb was completely dry when I put it in originally. I think the reason so little fuel spit out is the bowl wasn't yet full when I noticed it was leaking and I shut it off real quick. I think if I had let it fill the leak would have been more pronounced. I mean it was just a tiny amount of spray in terms of the amount of fuel that was coming out the air intake.