The user’s account limits have no bearing on your application’s API rate limits.
If you build an app that enables a lot of users to (for example) post low quality content at a high rate, then it may be write-restricted as that would be suspicious / abnormal behaviour. If you are simply enabling users to post Tweets normally via your app, there’s no reason to expect that the application would be limited.
To be clear, the account limits are documented here and the application API rate limits are here.