Covariance of Constrained Maximum Likelihood Estimators

I plan to numerically estimate the parameters of a GLM but with constraints imposed on some of the parameters. In this case, does the general approach of estimating the covariance matrix of my MLE estimators still apply? For example, those given by: https://www.statlect.com/fundamentals-of-statistics/maximum-likelihood-covariance-matrix-estimation

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