The objective function would not satisfy CVX’s DCP rules even though the optimization problem would be convex. I don’t know how to formulate that problem in CVX, although I am not saying it definitely can not be done.

If you do figure out how to get this accepted by CVX, please let me know, because I am interested in exactly this situation: maximum likelihood estimation of Multivariate Normal parameters subject to additional convex constraints. It would have to be a clever reformulation to get it accepted by CVX.