When was this?
The Constituent Assembly of Pakistan was an infamously incompetent institution which was so utterly unable to write a constitution that, after he dismissed the Prime Minister in 1953, in 1954 the Governor-General then dismissed the Constituent Assembly after a dramatic power struggle which saw a court case. This was, in many ways, Pakistan’s first coup d’état. Then a new Constituent Assembly was called in 1955, and in 1956 it wrote a new constitution. In 1958, however, the first President of Pakistan used the existing precedent to dismiss the legislative assembly, and he then declared martial law and ruled by decree with support of the military. Then the military subsequently forced the President out of power and established Pakistan’s first military dictatorship.
If this constitution making Pakistan a Commonwealth Realm is issued before 1953, that would butterfly away the first precedent for military dictatorship which would strengthen Pakistani institutions, though I think Pakistan’s Bengali majority and the horrific racism the Pakistani elite held towards Bengali speakers means some sort of institutional failure, associated with Bangladeshi independence, is inevitable. If that is not the case, and if instead the constitution is promulgated after 1953, then I think that would change Pakistani institutional weakness little. In both cases, in the long run, the monarchical link is unlikely survive.