No. The designers simply give you materia because it's a game. It has nothing whatsoever to do with the storyline.
You're saying that Cait Sith carries a
Manipulate materia by plain coincidence? It just seems a bit too much of a smoking gun to me. If I were designing that section I would definitely consider concealing hints in character equipment to intrigue and delight the player.
Current mystery - why Sephiroth throws the Destruct materia at Cloud.
Destruct is a dark, mean-sounding materia; Sephiroth is a dark, mean-kinda guy. I'm not sure what else would be appropriate for him to throw at this stage in the game (he can hardly hand over an Ultima or Contain).
I do think the destruct materia is linked to his Barrier/MBarrier use as a final boss, but in a more prosaic way: it gives the player an 'aha' moment when they remember that the materia Sephiroth gave them holds the key to beating him at the end of the game.
Relationships like that give the player clues what to do and pleasure when they recognise the callback. It's like when you use a brick joke in stand-up.
