The particular species of wood plays a factor but not as much as the individual piece of burl wood you plan to use. Some are tighter than others by species but being an unnatural growth of the tree there's no specific formation they follow. For example, Osage burl is highly sought after in the duck call world but they vary a lot; some are tight and perfect as they lay, others are loaded with voids and need stabilized and filled with resin before turning. Some guys like to stabilize any burl they work because the outer appearance of the blank isn't always what's on the inside, and burl can blow up easy.
Osage Burl, various Rosewood Burl's, Yellow Cedar Burl, and Amboyna Burl are all very common for use in duck calls and would probably make a fine trumpet. The right piece wouldn't necessarily need to be stabilized, but when working with burls it's never really a bad idea. Some of the softer woods even stabilization can't save.