Yes, that is permissable and done all the time. Here’s why. A Memorandum of Oil and Gas Lease is only a notice filed into the county records stating that an OGML has been taken from you. A Memorandum only has to state 5 things: (1) Names of Lessor and Lessee (with addresses), (2) Date of the lease, (3) legal description of the lands covered by the lease (including any depth restrictions, such as “only as to depths below the bottom of the XXXX Formation”), (4) rights being temporarily transferred from Lessor to Lessee (usually a variation of “right to explore, drill, equip, and produce”) and (5) the term of the lease (3 years? 5 years? etc.).
The addendum added to the unrecorded (considered the “original”) lease always remains in full force and effect. Just be sure to always, always store your copy of the complete, fully-signed original lease in a safe place. Better yet, store that original paper copy in a safe place (like a safe deposit box) AFTER you scan it (including the Addendum, of course) to create a pdf of it and store it on a flash drive.