Even if you obtain a waiver for a given article, you should still deposit the accepted author manuscript in DASH. It can be made available after a delay, or kept "dark" depending on the nature of your publication agreement. The OSC can help determine what kind of distribution is appropriate for the work.
If your article is subject to the NIH Public Access policy, note that your obligations under the NIH Public Access Policy cannot be waived. The same may be true of open-access policies at some other funding agencies. Look up your funder in the ROARMAP database for more information.