Hiding in plain sight works a lot better than one would think; my car keys do it to me all the time.
Wouldn't they recognise the cat and think that Shaft stole their cat, or something?
Though, either way, if they think that it's their cat or just a regular cat, that may save Dracula from being destroyed yet again.
But yet, stray cats are known to be killed by heros, by logic of FF6. I remember fighting stray cats some point in the game. They also make for a very good rage technique.