Thanks for posting to PX Community @jadkins.iiq !
They should NOT see the Engagement as they would no longer match the Engagement Audience Logic criteria.
PX Engagement managers can add more Engagement Audience Logic Rules to any of those Engagements that are “triggered” by CS JO Programs to target them more precisely. And, those Rules additional Rules will be respected when qualifying users to see them in-app.
Your use case is a really good one as these tracked User/Account attribute can/will change often and make some previously JO-queued Engagements, which is really what happens on the backend, unnecessary or out of date.
The most common additional Engagement Audience Logic Rule that I recommend is based on a specific URL and/or Product Mapper Feature being used “right now” to ensure that the CS JO-triggered Engagement does not play immediately the next time the user logs into the PX-tracked application. This will help ensure a better experience for end users and can help to to only show these in-app Engagements where they matter and are needed in-app.
Happy PX-ing!!!