Does having too many cck fields negatively affect site speed and performance?
Yes. The more fields you have, the more load you should expect on your database server; that's a given.

What it means in real terms depends on your hardware, configuration and usage - you'll need to benchmark your site in that actual environment to come to any meaningful conclusion. If you get one request a day, for example, your pages are cached, and you have a brand new shiny server, then you probably won't need to think about changing anything.

If you get thousands of requests per second, all your pages are non-cacheable, and your server isn't great, then you might have to think about re-structuring that data so it's more performant (e.g. creating custom field types to combine data from multiple other field types into a single table).

In short, there's no general answer to what you're asking. You need to see what problems your application develops under load, if any, and deal with them then. Premature optimisation is rarely a good idea.

All of that said, Drupal's main defence against this kind of thing is caching. There's a great post here: How do you improve Drupal performance?