I would doubt it would change much excelt for dialogue. They'll probably just stand and wait until you say yes, or just drag you into whatever was supposed to happen anyways. I found one example:
Professor Rowan: You two, you truly love Pokemon, don't you?
No: "Er-hem! I didn't quite catch that, so I will ask you again. You two. You truly love Pokémon, do you?"
Yes: "I will ask you once again. You two. You truly love Pokémon, do you?"
If you say yes twice you get a Pokemon. Saying no will just make him repeat himself.
It also happens in ORAS, when the evil organisation of your game threatens you on Southern Island.
By saying you'll help protect them and battle them, Steven will congratulate you and start a battle with you.
By telling them to go right ahead, Steven will say its no laughing matter and you'll still get pulled into battle.
Sources: 1 and 2