That's usually called a saddle mount.
And IME, no. Remounting after removing means rezeroing.
At least it does with the one here. That thing spent a few weeks on an 870 and since then has been on the shelf. The mount was acceptable but the cheap scope was not.
Not that this is limited to saddle mounts and scopes. When I remove a barrel from one of my slug shooting 870s, clean it and replace same, zero wanders. Some times not enough to take it off the paper at 50 yards, but enough to need
resighting in.
HTH....