Hi Rachel: tl;dr: yes, it is okay to delete the plugin. No, it won’t delete posts that were syndicated. If you have successfully deactivated the plugin already then deleting it won’t cause any damage.
Longer explanation: I’m sorry to hear that you had trouble getting FeedWordPress to work as desired. If FWP has syndicated posts, the posts it has syndicated are stored in the wp_posts database table just like local posts, and they will not be deleted or otherwise damaged if the plugin is deactivated or deleted. They will continue to appear just as they do while the plugin is deactivated. Deleting the plugin files will not cause any additional changes.
A quick note for others who may be reading this thread. I can be relatively confident that Rachel’s deleting theplugin won’t cause any problems, because she has already deactivated FWP and is apparently running her site successfully with FWP turned off. However, if you need to deactivate or delete FWP, while in general this shouldn’t cause any problems with the content you’ve already syndicated, you do need proceed with caution if you altered your themes to use FWP’s template functions or if you use common add-ons like FWP+: Add Attribution. Since both the add-on modules and the template functions depend on FWP being installed or active, trying to deactivate FWP while your theme files use FWP-specific functions, or while using an FWP-dependent add-on module like FWP+: Add Attribution can cause fatal PHP errors which will prevent WordPress from working correctly on your site. To avoid these problems, make sure that *before* you deactivate FeedWordPress, deactivate any add-on modules that depend on it (usually these are identified with the prefix FWP+ in the Plugins listing), and change your there’s template files so as to remove any FWP-specific theme function calls (like syndicated_link(), is_syndicated(), etc.)
HTH.
