Choppy playback affect export?

No, it will not.

However, choppy playback indicates that your system is not upto the task of displaying heavily edited video in realtime. That may mean that your encoding may also take (much) longer.

It is therefore best to find the source of your choppy playback. Most likely, your source footage does not match the one in the timeline. This in itself is already taxing on the system. Add any effect (such as a grade) and the burden quickly skyrockets... the same goes for adding a (de-)noise effect...