You didn't say ArcMap or Pro.
I haven't tried it, but if the datums are the same and it is supported (that is if it works at all) than there is no reason that would be a problem. If the datums are different I'm not sure the geotransformation would be fully supported, though it may be if the map you are editing is in in the coordinate system of the destination (paste-to) feature class.
This is the kind of thing that I would test before I started doing it in a production environment, even if the excellent @MelitaKennedy told me it was supported I'd test make sure it was working with my particular environment (software, version). (Trust, but verify!)
The way I would test it would be (you can try this with two coordinate systems in the same datum too).
1) create a point feature class in GCS NAD27 at an arbitrary location, say, -100, 40, and use the Add XY Coordinates tool so I could see the XY of the point.
2) Use the Project tool to create a new feature class in GCS NAD83. Be sure and use an appropriate transformation (say, NADCON).
3) Set the map to GCS NAD83. Go into the Map (ArcMap Data Frame) properties and make sure the same geo transformation is set up.
4) Get editing, and copy and paste the GCS NAD27 point into the GCS NAD83 feature class. Save your edits.
5) Run ADD XY Coordinates again
6) Compare the two
Good luck! Report back to the thread what you find out!