No, if you enable DiscourseConnect, users will only be able to login to your Discourse site through your WordPress site.
This may not be an issue for you, as it is not possible to allow users to login to Discourse both via Discourse connect and directly through the Discourse site. It may be a relevant issue if you have users who have created accounts on Discourse prior to your having enabled DiscourseConnect. For that case, as long as your WordPress site is using the default WordPress registration system, existing users will be found on Discourse based on their email address when they first login to Discourse via your WordPress site.
Have a look at Debug and fixing common DiscourseConnect issues. If you can not sort out the problem yourself, post a redacted version of an error log entry here, someone may be able to help.
I do not think the error you are reporting is a Discourse bug.
If you disable DiscourseConnect, users who have created accounts on Discourse via your WordPress site will have to click the “I forgot my password” link from the Discourse login modal and use the email they are sent to reset their password.