However, the CVX Users’ Guide is correct in this case:

trace_sqrtm(X) trace of the matrix square root of a positive semidefinite matrix X. which is the same as the sum of the squareroots of the eigenvalues. Concave. Outside of CVX, returns +Inf if argument is not positive semidefinite.

With such attentive reading as you have exhibited in discovering two CVX documentation errors, you should be in good shape for using CVX. You are hereby awarded a free virtual beer