I requested, from the US, my kids certificates of Citizenship. I asked that it be expedited, and had them back in 2 weeks.
I'm not sure if they were just quick, or if it mattered, or if it would work if it did matter, in the future.
But, always worth a try.
I also indicated, why I wanted it expedited, was that we were in the process of returning to Canada in the next 4 months - when my status should by current timelines be hopefully available, and I said something about insurance/their health because we'll be going to Ontario where they will have a 3 month OHIP wait already, with added time if the Certs took longer.