That can be done, but psychologically isn’t as optimal for collaborative brainstorming as pure brainstorming without analysis, if the maximal generation of new ideas is the primary objective.
“Yes, AND…” is applicable primarily to purely brainstorming to enhance the brainstorming. But analysis doesn’t necessarily have the effect of completely stopping everyone from brainstorming while analysis is occurring, as determining what is wrong with a concept before analysis is complete could inspire further brainstorming. Also, as you have suggested, the final results of a given analysis could result in inspiration of further brainstorming.
Brainstorming could hinder analysis if it gets too far away from the original topic of the analysis in a way that the analysis is distracted.
Discourse has what it calls linked topics, which allows you to create a new topic that is in part a reply to a post in a thread where such a reply would be considered off-topic. These linked topics are created by clicking on “Reply as linked Topic” locate to the right of each post.
So perhaps the best approach on the forums is to keep the topics in the “Evil Genius Think Tank” category purely brainstorming topics, allow topics outside of that category to have a mix of analysis and brainstorming, but have a/some new linked topic(s) created if the brainstorming in a given “brainstorming/analysis mix” topic starts to get off topic.
The “mixed” topics could start as a linked topic from a purely brainstorming topic (but doesn’t have to).
It is possible for a purely brainstorming topic to get off-topic requiring a/some new purely brainstorming linked topic(s) to be created, but as the subject of purely brainstorming topics tends to be more abstract, the requirements for determining if you are on-topic is not as rigid as with other kinds of topics.