When you indicate that you are Native American on the Common App, it asks you which tribe and whether you are enrolled. You need to indicate “No” as the answer to the enrollment question if you do not get the appropriate paperwork back in time. If you wish to clarify, then you should indicate in the Additional Information Section that you have applied for tribal membership, but the application is still pending.
However, since there is no need to even fill out the demographics section, you don’t need to list your Native American heritage at all if you don’t want to. It would not be lying - it is information that is up to you as to what you choose to disclose.