Yes, joke questions are allowed on April Fools.
In recent years, the best posts have been allowed to stay up on Meta and RMT even after April Fools. The April Fools posts of lesser quality/effort will be hidden after a few days. April Fools posts on the main site are usually hidden, much to my dismay.
Recently, I've been adding them to this tag as I've come across them; check it out if you want to see.