This is based on an old classicMx trick that I used a lot in writing stealth model code

I think you can constrain the calculated matrix to be equal to a free matrix and the obtain CIs on the free matrix. for example:

mxMatrix( type="Full", nrow=nvar, ncol=nf, free=TRUE, values=.3, name="factor" ),

mxMatrix( type="Diag", nrow=nvar, ncol=nvar, free=TRUE, values=.3, name="residual" ),

mxMatrix( type="Stand", nrow=nvar, ncol=nvar, free=TRUE, name="Vconstraint" ),

mxAlgebra( expression=((factor %*% t(factor))+(residual%*% t(residual))), name="expCov" ),

mxConstraint( alg1="expCov", "=", alg2="Vconstraint", name="Constraint1"),

When you lookthrough the output of the Fitted model the elements within the Vconstraint matrix are shown as estimated. I'm pretty sure this means you could CI them but I haven't tested this