Crazy Egg Asynchronous JS tracking slow down page load? [on hold]

We are working with an external developer who is advising against installing a Crazy Egg tracking code in a website because he says it will slow down page load...

Is there any justification for this?

I believe there are other reasons for this advice but happy to be wrong if there is some truth in this. The crazy egg website deals with this question but as you'd expect they dismiss it as an issue.

We will test two versions of the site to see if there is any difference but interested to get some thoughts on this.