Cheryl herself gave a legit compliment to Archie's plan when he told her about his scheme to fake being boyfriend and girlfriend. And that'll be key. When she wrote off Archie, she just as saw him as some small town yokel boyscout peasant not even good enough for her high heel sole. When she goes on her sham affair with Archie, she'll see more of the Archie who rescued her from her birth father and whipped up their scheme. The cunning on his feet, driven, protective, Archie. And that's what'll draw her in. It fits with the pattern that each of Archie's girls was drawn to him for different parts of him (like Veronica seeing a boy who'd both treat her like a queen and treat her like a best friend) and she could even treat him as something of a Replacement Goldfish for Jason.
When the hour comes for Archie to "break-up" wth Cheryl, the redhead lady will try try...and find she can't go through with it. Tell Archie she wants to be with him, for real. And Archie will be flabbergasted, yet still resolved to end it. He'll remind Cheryl he's already seeing someone and she'll wave it off (complete with telling Archie to break-up with her instead). Obviously she won't succeed in taking Archie and will hold a grudge against both him and his girlfriend Sabrina (whether Cheryl knows about her or not).
What happens from here is iffy. If Cheryl knows about Sabrina she can certainly inform Betty and Veronica about her out of spite. If she doesn't, she can use her resources and connections to look into Archie's private life. In either case, she can know about Sabrina's relationship with Archie and even force another Enemy Mine situation, this time over Sabrina.
