Presidential Succession

[ATFFL]

No. "Officer" in context means "officer of the United States," which does not include members of the legislative branch.

Under Article I, Section 6, Clause 2, "no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office."

It's funny that you quote that, while saying 'yes' to the poll question. The text makes it clear that a federal legislator may not be an officer of the United States. "Officer of the United States," then, must not include members of the legislative branch.

It seems to me they can be, so long as they lose their membership in the House or Senate.

[ATFFL]

What are you talking about? An officer of the United States can not be a member of the House or Senate. It's obvious, then, that a member of the House or Senate is not an "officer of the United States" within the meaning of the Constitution.

No, and the provision quoted by Emsworth makes that clear.  Otherwise anyone in Congress would be an officer and would be required to give up their seat in Congress.

Being the President does make one an officer of the United states.  So, to be President, one must give up their seat in the House or Senate.

However, being in the line of succession to the Presidency does not make one an officer of the United States until the line reaches that person and they accept the position.  There is no office of "Third in line to the Presidency" and so forth.  Thus being in the line is not being an officer of the United States and a member of Congress can be in the line with the understanding they will lose their seat if they are ever called on to step up to the executive office.