The Pilot said:
Definitely able to but would require cutting into stucco on about 20 of 22 windows.
Understood. I can tell you when I'm replacing windows in masonry, I remove the brick/stone/stucco every time so I can properly tape and flash the windows. Otherwise, you're putting a lot of faith into the "pookie" and the person applying the caulk. You can trim it out but, as said, it's tough to make it look good in stucco retro fit.
I'd also suggest that you insist the contractor use a good sealant like NP1 over a cheap one. It'll blend better with your stucco anyway. Then be sure to check for dry or cracked sealant every couple years and replace as needed.
I have done flangless, but only in areas that are totally covered by a structure and has no way for water to intrude.
Anecdotal story- we were brought into a remodel where the client previoulsly had all the windows replaced in a big 115 year old brick house. All of the windows failed. They opted to do flangless and it led to major issues, including a major mold issue. We removed the brick around the windows and replaced with flanged windows and the problem was resolved. Its a pain in the ass but, imo, the right way.
One thing to check is if your existing stucco trim pieces are actually efis (foam). A lot of times I find the foam to have totally disintegrated leaving only a paint shell.