The difference of means as a fulfilled precondition for a mediation analysis

The preconditions for a simple mediation analysis according to Hayes (2013) are statistically significant associations between X (the independent variable) and M (the mediator) as well as associations between M and Y (the dependent variable). In the case of a dichotomous independent variable with the values 0 and 1: could a significant difference of the means in M between the two groups 0 and 1 be considered as a fulfilled precondition/significant association, so that carrying out a mediation analysis is justified?

My own thoughts on this question: Firstly, the term association confuses me. Unfortunately Hayes doesn’t give a definition of “association”. Other sources that I have consulted yet define association as covariation and link it to correlation and regression. The difference of means isn’t mentioned as a measure of association. But doesn’t the difference of means also indicate covariation in certain cases? For example, I have a dichotomous variable that indicates membership in a trauma survivor or a non-trauma group. If I find significant differences between the two groups in an outcome like depressive symptoms, I could interpret it as the following: depressive symptoms covary with trauma exposure; therefore the difference of means is an indicator of covariation. Furthermore in a linear regression model with an independent dichotomous variable (values 0,1), the non-standardized regression coefficient is the difference of the means of Y between 0 and 1. The regression coefficient is considered as a measure of association. As a result, in a regression-based simple mediation model with X as the dichotomous independent variable, the path coefficient from X to M is the difference of the mean of M between 0 and 1.

Thank you for your response.