A CD drive at the time would have costed about $100 more. Nintendo ain't losing money on hardware.
So, maybe they would have gotten more market share, but ultimately Sony would still win I think.
Prior to the PS1 no console had crossed the hundred million mark. Including Nintendo's systems with all that third party support. The success of the PlayStation wasn't only about third parties. They made the system happen with a lot of great marketing and momentum. Even with a CD drive, Nintendo would still run into other problems, like their youth focused image and so forth. Sony expanded the industry back then.