Is there any legal reason Ryan could not serve in the House and as VP at the same time?
Yes.
Article I Section 6 Clause 2
No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States which shall have been created, or the Emoluments whereof shall have been increased during such time; and no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office.
This is also why we don't have members of Congress serving as Secretary of State or the like.
Secretary of State is more clearly unconstitutional because it is an appointed office.
Why would VP be considered "an Office under the Untied States" when Senator or Representative are not? I don't think you can separate the first and second parts of this to apply to different sets of offices - they are meant to say that you cannot serve both, no matter whether you were elected or appointed first.
