Can this crack in the steel chain-side dropout be welded?
You need to consult in person with someone local to you who can make a qualified recommendation.

"It is Steel so can be welded"  is mostly true, but there are always exceptions.  A good welder will give you their professional advice.  Don't bother asking someone with a stick welder in their garage.

I've personally just got a quote on welding a crack in a seat tube, and that came in at $100 NZ.  The bike cost me half that to buy, but I can't replace the frame for anything like that.



When you do find someone local, prepare the frame by stripping everything off the bike.  Everything that is not frame needs to be removed, and you should cover and protect all the threads/bearing surfaces with rags and tape. 

Yes, I would remove the fork and headset, and the bottom bracket, leaving just Frame and Paint.

The only non-frame thing I might leave in there would be an old scrap axle bolted into the dropouts, to help keep everything in line and not getting extra-stressed while manhandled.

Also, clean the bike.  Noone likes getting dirty, and your welder is more likely to agree if its not filthy. 



If the welder suggests unbrazing and replacing the dropout instead of welding, then you should take that advice.   They may suggest a sleeve or fishplate for strength — take that advice.  Figure out if it will interfere with your chain/cassette or fitting of the rear wheel.

And lastly, if its not safe to fix, or if its super expensive, consider retiring the frame and put those costs toward another bike.