I don't think this would work well.
Generally, on the Stack Exchange network, we expect questions to have objective, quantifiable answers - and a limited number of them.
One of the universal close reasons on every Stack Exchange site is "Too Broad":
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question.
Questions that have an unlimited number of answers are almost universally closed. This type of question would allow an unlimited number of answers - each conlang could get at least one answer, and "answers presenting a new ad hoc conlang" would only exacerbate that.
That already makes me wary - that there would be an unlimited number of possible answers to this "challenge".
Now, while there are sites that have "challenge" questions, such as Puzzling.SE, they have specific rules for regulating them to fit on the site. Questions on Puzzling.SE that don't have a clearly correct answer are closed.
If we take a look at the help center, we'll also see some guidance:
Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page.
This is basically the definition of an "open-ended" question, where every answer is equally valid.
The type of questions that you're proposing seem like they'd be too broad, not useful, and not a good fit for the site.
Aside from that, though, the goal of the site is to create a repository of useful questions and answers about constructed languages - both existing ones and ones that people are creating. These don't seem like they'd fit into that goal - they'd be providing a sort of "fun challenge" for users, but they don't actually help the site.
In fact, there's the possibility of hurting the site. If you have a fun, easy, but not the main point of the site type of question to ask, it can quickly grow and take over the site, drowning the site in these and making people uninterested in the site. See identification questions on Movies.SE and Anime.SE - they were flooded with low quality questions for years until they banned them. These seem like even less useful and lower-quality than identification questions.