The effects of multicollinearity/redundancy would be similar as in multiple regression analysis since a mediation model consists of a series of regression equations. For example, you might end up with large standard errors or suppressor effects. See, e.g.,
Maassen, G. H., & Bakker, A. B. (2001). Suppressor variables in path models: Definitions and interpretations. Sociological Methods & Research, 30(2), 241-270.
MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding and suppression effect. Prevention Science, 1, 173-181.
this depends on the exact pair/set of variables which are colinear. If it is the relationship between X and M (the mediator) then this will do no harm, as it will be represented as a strong direct effect. If you have two Xs, then colinearity will lead to unbiased effects but large SE (thus, low power) and wide CIs.
If you have two mediators, you should run an SEM anyway and if you estimate the error covariance between both, this will capture the colinearity (that is not due to the common influence of X) and everything will be fine.