No.
What did he win without Taylor.
He won a couple of league cups in the late eighties and managed a couple of third-placed finishes. Remember that, at this stage, the reform had come into effect whereby home clubs kept all gate receipts. Also remember that broadcast revenues and commercial revenues were pretty negligible at that point. Forest weren't in the top ten in attendances and drew about 50% of the gates of the wealthiest competitors such as United and Liverpool.
He definitely had them punching seriously above their weight throughout the eighties. Sure, in the early nineties his alcoholism really took hold and he basically lost it. But he was a bloody good manager for around a decade after Taylor left him. The changing circumstances of football finances, with the odds stacked against Forest in a way they weren't in the seventies, meant he was never going to win to the same degree as he previously did, whether he'd had Taylor with him or not.