Mitchell,
First off, I'll be moving this post to the JLinked - Joomla 2.5 support area after I post this. Just want to make sure you find it properly later.
With v1.3, no, there's no way to bypass the registration process altogether. With the next release, v2.0, we'll have an automatic registration process. That feature has been a part of JFBConnect (for Facebook) for years now and is wonderful. It wasn't possible with JLinked until LinkedIn added the ability to capture email address. We simply didn't have enough time to implement and test the automatic process in the v1.3 release and wanted to get something out that supported the new email abilities ASAP. With that said, yes, if you hide everything, right now, the registration form can be pretty much empty. In that case, we'd still recommend showing something to the user (even if it's just username), so it looks like they're able to modify and/or approve the account.
As for the Login form, yes, that's to link a user logging in with LinkedIn to their existing Joomla account, if they have one. If you hide the form, the user would only be able to register, which would create them a new account. In the v2.0 release, we'll have an auto-link by email option where, if the user's LinkedIn email matches the email of an existing user, the registration form will be bypassed and they will automatically be connected.
Before you ask, v2.0 is expected in the ~November timeframe.
Hope that helps explain,
Alex