As the Constitution does not explicitly state that the speaker must be an
incumbent member of the House, it is permissible for representatives to vote for someone who is not a member of the House at the time, and non-members have received a few votes in various speaker elections over the past several years.
[10] Every person elected speaker, however, has been a member.
[9]
If it is true that Kari Lake and General Mike Flynn heard him say he would serve as Speaker, then yes, that is major news.
It does NOT mean it will happen, but it would be major news nonetheless.