I see two different elements to this hobby, watch collecting and watch building.
No offence intended to anyone, but personally I just don't get the 'look at me I'm wearing a Rolex" thing so the branding in that sense doesn't matter to me. However, if I'm putting together say a Rolex collection and the only way I can show a 5210 & 5217 is with a good rep I'd have no issues in saying that it's a replica.
My interest tends to be more in putting together a replica of an interesting watch where parts identical or very close to the original are findable with diligent searching, to build something unique and usable that's as good if not better than the original, and for a price that's only a fraction of what an original would be ............... if you could find one and if you would ever then dare wear it.
In that sense the branding is not important (to me, ymmv) and in fact making a sterile version can have advantages.
This is very much along the same lines as how the Replica or 'Kit' car enthusiasts work. Very few owners in the privileged position of being able to find and afford an original Porsche Speedster or Ford GT40 would be willing to use it as a daily driver but the replicas make ownership and use of something very similar, possible for many enthusiasts. Owners of say a Chesil Speedster will proudly let you know that it's a Chesil, in a similar way to how some rep makers have a reputation all of their own - JZF, JL, DSN etc.