The answer to this one is straightforward: no in 99.9% of cases.
The lineage societies do not require it.
Some states require you to purchase a certified copy every time you want to request a certificate. However, it’s not required by any lineage society of which I’m aware. If an information copy is offered, go ahead and get it…
And before you order anything, be sure to check what’s digitized and available online. For Pennsylvania, start with Ancestry.com. The site has many vital records for the early 1900s. The Rhode Island State Archives is now a record goldmine. Finally, FamilySearch is always a wonderful option. Yes, you can use digitized records for applications!
However, you may need it to get a copy of an ancestor’s record.
The one exception: if you need to request a direct ancestor’s birth certificate from the New York City Health Department, you may be asked to provide a certified death certificate.