I totally understand. When there's an imposing time limit, somethings need to have higher priorities and such :p
I mean, that decision is ultimately up to you, especially depending on how you want your game to feel, I've seen both styles done with very good success. If I were to take a guess, I might go with having a flashing overlay on top of the boss sprite too, in lieu of a healthbar. That would give more than enough feedback for the player. One of the beautifies of SHUMPS is the tension that kind of builds during a scene. So like, for example: if a player is in a boss encounter who happens to have really erratic patterns, or launches a lot of projectiles, without a health bar, every hit of damage the player throws out leaves this looming feeling of "how much longer do I have to go?" . It forces them to have to remain on their guard instead of falling into a reactive lull.
That's how I see it / my two cents anyways! Hahaha!
Yeah, you have a good point. Heck, this whole jam taught me a lot about the original hardware of the GB. It really gave me a whole new appreciation for the things people have made on it, both officially and unofficially given its limitations!