My take on Quinn is that she's adept at manipulation and power plays and rarely is bothered by the paths necessary to get what she wants... having a genuine interest in Chad? Hell no. Being willing to manipulate Chad as a backhanded route for future manipulation of Sage? Hell yes, I believe she's capable.
*Note- Also considering the fact that Chad is apparently incredibly sexually impotent Quinn wouldn't really have had to get her hands dirty with him to manipulate him... and who said anything about imagining her as being passive? Quinn seems like the kind of girl who could seriously multitask by doing her homework/prostitution scheming while "having phone sex" because she's great at acting and focusing on important details while tons of shit happens in the background.
Yeah let's make an assumption of this : What will Quinn benefit from this? Quinn is looking to get her business bigger and get more money, also she can be interested in a better status. Sage will already graduate next year, so she doesn't need to risk it because of this.
Sage is not the HOT president because she is Chad's gf. Chad means shit in powerscale. Sage being obsessed with Chad's lover has no benefit whatsoever to Quinn.
Stop trying to point everything to Quinn just because she's shown to do "questionable" things. Not everything is because of one person, try to think bigger. Everyone here "theorizes" stuff and for some reason, it's always Quinn