Pretty much, but that explanation is way more complicated than it needs to be.

The image of "trickle down" compares money to water. If you drop water somewhere it will move downwards. But for some reason when people talk about trickle down economics they think that money will trickle down from the people will lots of money to those with no money.

If you go back to the image then water will trickle down to the place where all the water has ended up before, i.e. the ocean. Expecting money to trickle "down" from the rich to the poor is like expecting water to trickle "down" from the ocean to the mountains.

And there are lots of obvious reasons for that. A poor person will have to take a loan from time to time which means that they have to pay for no lasting value in return. They will also have less opportunity to save money by buying things in bulk or waiting for discounts. A rich person on the other hand has little reason to pay workers for something that does not end up making them more money.