What I heard was that the Challenger wasn't in a fully serviceable condition but it had the female teacher amongst the crew and it was the case that any delay to the launch was unacceptable.
If you are saying they launched simply and only because of the teacher (Christa McAuliffe) was on board and the “teacher in space” project, and that if she hadn’t been there the launch would have been scrubbed then the answer is no.
Fundamentally there was a political/management need from within NASA to launch but that was almost entirely down to the fact that Senior management wanted to show that the Shuttle programme, aka the Space Transport System (STS), had evolved from an experimental project into a reliable transport system that could operate to a schedule with pretty much fixed, predictable launch dates (edit to add - and they were struggling..as PDR correctly points out below there had already been multiple delays to the flight..management were feeling the pressure). There has never been any suggestion that they launched simply because Christa McAuliffe was there.
As far as the shuttle not being serviceable when launched, well there were relatively, in the scheme of things, minor niggles (what would probably be called “allowable deferred defects” in airline speak ) but of course the major issue was launching outside demonstrated limits (temperature) and a questionable design feature.
Rogers report below:
https://spaceflight.nasa.gov/outreac...ion_report.pdf