I see this question come up a lot, and I've had to dig up the answer more than once, so I'm posting it here for posterity.

The answer is yes. For example, if you're playing a Nano in Numenera, and you want to activate an esotery, but your Intellect Pool is at 0, you would then spend might.

Here is a link to the Google+ thread where Monte Cook clarified this.

Here is a quote of Monte's post:

It's the intent of the rules that points come out of pools in a certain order of operation, but that as long you obey that order of operation, you can keep spending points. It's just like with damage: you lose points from your Might, and when you have no Might, they come from Speed, and when you have no Speed they come from Intellect.

This means that while yes, esotery power (and Effort associated with that power) comes from Intellect, if you have no Intellect, it comes from Strength. And if you have no Strength, it comes from Speed. So that means someone could indeed harm or even kill themselves by performing esoteries (or other abilities) over and over.

But you should play the way you want. This sort of corner case isn't covered explicitly in the rules.