I am currently in Poland on a business Schengen visa, I am a spouse of a Polish citizen, and I am applying for a temporary residence permit. Since I cannot receive a stamp in my passport, will the stamps be given at a later date after ...

.... re-opening the customer service?

If your application is formal error-free, as soon as we resume our customer service, you may receive the stamp in your passport.
The stamp is dated on the date of application, and not on the date when you receive it. Nevertheless, this does not mean that your Schengen visa time limit will be suspended. Staying in Poland during the ongoing procedure for the temporary residence permit is not deducted from short-term stays based on Schengen visas.