No, because the Nate Grey that appeared in X-Man #5 and beyond was the same character that was in #1-4 just transplanted from an alternate reality. Just like Dark Beast, Holocaust, and Sugar Man.
Actually the correct answer is, the after House of M heroes are the SAME
heroes that were in House of M except some have memories of the event and some do not. In fact it appears large portions of the people on 616 remember HOM and Captain Marvel by name unlike AOA afterwards. See post below for crowds chanting her name.
That's from Giant Size Ms Marvel #1 AFTER
in the 616 universe.
Dark Beast was a name change after
Age of Apocalypse just like Captain Marvel changing her name after returning to the 616 universe as Captain Marvel. In X-Men Alpha he goes by McCoy. In Factor X 1 he's even identified as "Beast" and continues by that name throughout the series in additional issues thru #4.
At this point it's just plain common sense
that the first
time Carol Danvers went by the name Captain Marvel was in House of M. AS9 isn't the first, it isn't the second, it isn't the 3rd and it may not even be the EIGHTH
. I still have a lot of side stories during this period in other titles to work thru.
The question is which one counts as the First Full Appearance assuming HOM3 is only the 1st and not the 1st Full.
The facts and dates are above, a clear and exact timeline
showing the progression in order from Warbird to Captain Marvel to later going back to Ms Marvel after
many issues published as CM.
I'll have some more scans for you later when I have more time.