Can I ask a Fermi question on Physics Stack Exchange and looking for creative and plausible answers? Even that may sound silly? Such as: How much sea level will it rise if you pee at the sea?
There are two problems with Fermi problems here.
First, this site isn't meant to have open-ended questions, or challenge questions. Answerers aren't meant to be competing against one another for the most interesting solution. Rather, we answer questions in order to build up a knowledge base and help disseminate facts and results in physics. Many Fermi problems have multiple acceptable answers depending on what assumptions are made, and this platform simply isn't designed to handle such cases. Remember, there can exist insightful/entertaining/good things in life that are nonetheless off-topic for this site, and there is nothing that needs fixing with this state of affairs.
Second, and more subtly, many Fermi problems simply aren't physics. The classic "how many piano tuners are in Chicago?" is a prime example of this. The solution is to make educated guesses for some input parameters, and then perform simple stoichiometry to convert units. This might demonstrate rational thinking, and it might require a decent background in everyday life, but it really isn't physics.
If a Fermi question is objectively answerable, is not posed as a quiz for the site's userbase, and is actually about a physics concept, then it is okay. The question must stand on its own; taking the form of idle musing purportedly had by some long-dead physicist is not sufficient to make a post on-topic.
I'm inclined to say no. This probably falls under the part in the help center where it talks about asking practical, answerable questions based on actual problems that you face; now, that's not meant to be interpreted too literally, but the reason it says that is to discourage precisely these sorts of just-for-fun puzzle-type questions.