No, in a normal non profit, compensation is generally not tied to donations. The CEO is paid a direct salary, he doesn't decide what to take based on donations.
The value that the Shliach/Shlucha brings to their organization, (usually) vastly outpaces the salary that they take. Based on comparable organizations they would be justified in taking a larger salary.
The amount fundraised (usually) suppresses salary and not vice versa.
In almost all Chabad organizations the Rabbi and Rebbetzin receive a salary from the organization.
ETA. I assume it would be unusual for a MO Rabbi to go into personal debt for their organization, while it is not that unusual in Chabad.