Yes, you can run in the floor joist, if it runs that way, or create a bulk-head (soffit) to run them in as well...
Also, if you're gutting the first floor, I'd get rid of the cast iron and replace it all. You've gone that far... don't leave that old stuff in there. It's a pain to tie into the cast iron with the no-hubs every spot you need to. Plus, if the cast iron is looking thin in spots, or has leaky spigots, this is the time to do it, while the walls are open. I ripped mine out from basement to roof: rent a chain cutter, only takes a few hours if you already have it exposed. It will make the rest of the job so much easier...