Yes, it works this way. From the cosmetics FAQ (https://forums.mtgarena.com/forums/threads/53744):
HOW WILL CARD STYLES WORK WITH ROTATION?
After the fall set rotation, you will have ways to continue to play with all the cards in your collection. This includes using any card styles those cards may have.
Additionally, if a card is legal in a particular format you will have the option to use any card that has the same name as it regardless of the illustration. Card styles for the older versions of cards reprinted with new illustrations will still function if you’re using the older version of the card in your deck.
For example, once Core Set 2019 and Rivals of Ixalan rotate out of Standard, you will still be able to use your copies of ...
Read more