yes, no and maybe.
My understanding of being eligible to be enrolled is that you must use PAPER documentation (not dna testing), which proves your connection to a prior enrolled member. I believe anyone with an adoption is going to show the adoptive parents, which would halt the process right there.
That is for enrolling.
As for knowing your history, that is not the same thing at all, and info that was given to you, is the key. As long as the grandparents are not living, then you can access records ie census, so forth that will give you more data, and verify what you were given.
Are you aware of, or in contact with ANY relatives from that side who are still living? If they are not blocked, and your statement of the grandparents being enrolled is accurate..they should be able to get confirmation of that from the tribe.