How to seam new stucco to old stucco when patching large areas
My authority is that I've researched and performed this very task in the past. That doesn't make me an expert, merely someone that had to deal with this.

For starters, I'd suggest getting actual stucco mesh/lathe rather than chicken wire. Neither are particularly strong, but stucco mesh is quite a bit heftier than chicken wire and is specifically designed to 'bite' the scratch coat and keep the stucco in place. 

It may  be overkill, but I'd also put a few stainless screws in whatever mesh you are using (rather than just staples) as staples would eventually rust. 

The screws on the existing stucco...at worst, it won't hurt, and at best is probably a good idea. 

All that said, the joint between the new and old will eventually show a crack/seam. Not a whole lot you can do about that. What I did was let the new patch cure for about a year, then came back and filled the seam with masonry caulk, and repainted.