No... if you touch the petals, you fall asleep. It would be really hard to refill the jar. Just holding it makes me tired.

[Pauses, then,]

I guess, logically speaking, you could set the jar under the tree and wait for petals to fall into it? But someone would inevitably see that, right?

[Plus, he has the Senku alibi too. Also the alibi of anxiety about souls in a jar.]