My thought is "no", but wanted to see if anyone had any information on this.
I would assume the versions simply control how you can interact with the features in Salesforce (ex. methods you can use, object/field access, etc).
Assuming you have a customization-heavy org, is there any performance benefit (transactional or deployment) for being at the latest API version (47 currently) versus 10-15 releases behind (ex. 32) across all your custom components (trigger, apex classes, lwc, VF pages, etc)?