Could it have been possible for the Moon to be split without any observable effect on Earth?
No the energy required to do this would cause the moon to melt.
However the story of the spitting of the moon supposes a supernatural cause, and one which is not bound by the physical laws.
God could split the moon and put it back together by his word. And God could arrange so that only some people saw it and others looked away.  When you bring God into your explanations the answer is always &quot;yes he can&quot;.  That's what being omnipotent means.