Yes, it looks like a Carrera 2447/3647 case, from as early as 1964 to potentially as late as 1970 in the case of the 2447.

The caseback is more of an open question. I have seen an early Carrera offered once before with this caseback, but the vastly more common style is a stepped, flat caseback, like this:

The Carrera was launched in the same year as Heuer acquired Leonidas (the aforementioned 1964), which muddies the waters a little. The caseback on your case is stamped Ed. Heuer (i.e. pre-merger) whereas the one I linked is Heuer-Leonidas SA (so post-merger), but we do sometimes see Carreras with pre-merger movements and cases - on my part, I believe they would have kept using parts from stock until they ran out rather than junking the Ed. Heuer-stamped pieces, because that makes much more commercial sense.

The caseback looks genuine, not questioning that, only whether it belongs with that particularly case. I believe the 404 (one of the pre-Carreras) used this style of caseback, but I don't own one to check. So I guess it's possible that very early Carreras did use this style, or it was used in pre-production, but it's not what we usually see - sorry it's not a definitive answer.

Mark