Lord of the memes

Of course not! Just because he didn't write it doesn't mean you can't imagine it. It just means there's no precedent for it, so you have to be creative

Morgoth did indeed have a body for the entirety of the war of wrath.

I believe that in Tolkien's writings, the only Ainur that lost their bodies were Sauron (during the fall of Númenor, then when the ring was destroyed), Saruman (killed by Grima), Gothmog (killed by drowning/stabbed in the fountain during the fall of Gondolin), Durin's Bane (killed by Gandalf the grey), and possibly an unnamed balrog (if indeed dead, then slain by Glorfindel during the fall of Gondolin). There's some mention in Melkor's Ring(?) that during Melkor's first chaining, his original body was slain, but I'm not sure if that's backed up by other writings about his first chaining. Regardless, it's a pretty small club of fëa separated Ainur, so I'd think that if there was a benefit to splitting from the hröa, it would be made clear