At least a day passed between the dropping of the stone and the first Orc attack in the Chamber of Mazarbul, and while Gandalf is certainly uneasy after the stone, the Fellowship are still able to have two nights' sleep afterwards - one immediately after, and one following an 8 hour march and in an open hall. That's not a sign of a company that's overly concerned about an immediate threat.
Furthermore, Gandalf's "death" in Moria was foreseen for a while, notice Aragorn's remark when the topic came up:
'You followed my lead almost to disaster in the snow, and have said no word of blame. I will follow your lead now - if this last warning does not move you. It is not of the Ring, nor of us others that I am thinking now, but of you, Gandalf. And I say to you: if you pass the doors of Moria, beware!'
And also after the Fellowship leave:
Did I not say to you: if you pass the doors of Moria, beware? Alas that I spoke true!
Gandalf himself takes responsibility for the fact that the Fellowship were trapped by Orcs:
'Trapped!' cried Gandalf. 'Why did I delay?'
While Pippin was certainly a "fool of a Took", one gets the sense from reading the relevant passages that Gandalf's fall in Moria was something that was fated, and both Celeborn and Galadriel also seem to think the same; as Galadriel notes:
Those that followed him knew not his mind and cannot report his full purpose. But however it may be with the guide, the followers are blameless.
There's finally the fact that if we do assign blame to Pipping for "killing" Gandalf, we must also give him credit for setting-up the situation that allowed Iluvatar to step in and create Gandalf the White, without which many things would have gone worse.