There might be some internal fighting as Goblins murder each other for higher positions, though I think everyone else is right that they just become a better target for war after their head honcho dies.
Mechanically, goblins don't change - as in they don't lose their immortality or anything like that.
Elves are the perfect military-strategy bloat race though due to their immortality and rigid social mobility, even despite the terrible grade of weapons they wield into battle on the back of additional animal reinforcements. Its also not uncommon to see goblins under modded settings also be greviously wounded, missing eyes, fingers, limbs and the like for their relative fragility in the face of enormous war enthusiasm as often old veterans will immigrate to a fortress being notably historical at all for not dying as chaff en-masse.
I'm pretty hyped for eventual DF assassinations, as destroying clowns can be circumnaviagated by eventual team-ups of nations assailing the obvious evil threat, but immortal warlords are much more substantial targets because right now there isn't really anything distinguishable other than staying in the role for a long time. Normally i throw goblins a friend to lean on as a buff, simply because [BABY_SNATCHER] is just a big dogpile without deep risen factions, its funny to see the reverse dogpile too, or babysnatcher mercenaries come in to avert the 'Order-Tide' problem vanilla df has at the moment.
Do goblin civs always have a Demon Lord?
Initially, yes. That's the only way they can spawn in worldgen (well that and underworld breaches, but those are pretty rare except in longer-lived worlds). If you set number of demon species in advanced worldgen parameters to 0, that world won't have any goblins either.
In regards to the OP's query: could also just be the fact that goblins tend not to be exceptionally strong individually compared to dwarves or humans (basically just being green-skinned elves that can work with metal and stone), so without a demon lord to hide behind they become easy pickings for other civs.
Demonless underground breaches don't strictly stop goblins from emerging, they will just be a native army (since without these, the bottom of the world is full of [EVIL] races within civs aka. goblins on vanilla) and set up that civ's dark-fort government afterwards in the occupied fort if they win, but on the flipside you can fully customize the master position from the start without the awkward inheritance from the spire founding demon. Makes for nice emergent "hidden" civ threat mechanics when it doesn't fluff up (which there is a high risk of happening, like spawning in a mountain-hall and being boxed in by a full strength dwarf-fort to the outside)