Until we get a pokemon with a natural 999+ attack, yes.
If a Pokemon is at level 100 and it has the highest possible attack for it's species, does Belly Drum do anything? If so how does it increase?
Until we get a pokemon with a natural 999+ attack, yes.
Stat-raising in battle is not limited by a pokémon's "highest possible attack for its species". That's only its highest possible natural attack. From there, stat-raising moves can boost it up to four times its natural value (which is what Belly Drum does in one move, at the cost of half your life bar.) I can't say with any certainly that it's possible for a stat to be so high naturally that the game won't let you make it 4x in battle.
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Pokémon GO: Level 37, Team Mystic
Rudoku: The 999 stat cap doesn't exist in RSFRLG, meaning with stat boosters you can have a calculated attack of over 999 (Huge Power Azumarill has something like 1700+ Attack after a Belly Drum).