And you would like to try and strengthen your application for that university? I listed the offers to the university but said that I wanted to apply to their school which meant me rejecting my offers, taking some time to prepare for the GMAT and apply to them for entry to 2021. I just wanted to make sure that I have a chance at their university. I also asked them if they could review my profile.

I think it's a good tactic

It honestly depends on the gap between the schools you've gotten offers from and your first choice. If they are well-known schools that the first choice would have heard about, then yes, this can help.

However, if they are no-name schools I don't know what this could help. I can't think of many ranked MBAs that do not require the GMAT.

In any case it is good to ask them for a precursory profile review to see if you stand a chance. Delaying for a year is not a step to be taken lightly.

This is a good point. It's only worth mentioning better or similar schools.