It is hard to know about this relationship, etc. I think it is possible they weren't lovers, as Catherine might have known how Peter the great would react to that, I would think. He would not have anything to do with his once mistress Anna Mons after finding out about her infidelity. Surely Catherine knew that would be a dumb thing to do, I would think. But, she was a very brave woman, and not very inhibited as her short reign proved, so maybe she thought she could get away with something or thought she would could be lovers with him, and it would not hurt. Both she and Peter did drink, but that didn't prevent Peter from accomplishing much.
It is thought Willem was in love with Anna not her mother. Catherine was however involved in he and his sister's corruption scheme. This was never a matter of infidelity, this was a rumor of diplomats in the court. But Peter had fought corruption all his life and then found his closest companion was part of it.