Do Overnight Reverse Repo Purchase (ON RRP) counterparties receive yield on the Treasuries that they are holding overnight?

Question

When a Money Market Fund or other counterparty buys an RRP, they are receiving an interest bearing asset. Do they earn interest on that asset as well as the ON RRP rate which is published at the New York Fed?
I presume not, but seeing as they are in possession of an interest bearing asset or basket of assets, it seems possible.