As stated in Lightroom Classic catalog FAQ "A catalog is a database that tracks the location of your photos and information about them. When you edit photos, rate them, add keywords to them, or do anything to photos in Lightroom Classic - all those changes are stored in the catalog(1). The files themselves are not touched."
A) A catalog can embedded information on images in different locations.
B) Lightroom can move files from one location to another one
C) Under Lightroom the preferred organization of images is done by collection, these are collected logical links to images. Operations on collection do not affect the location or the physical files.
D) In Lightroom, exportation can be either:
1) Exportation as new files:
This "burns" new files from the image file and the processing made.
The new files are no more related to the original ones, except by name.
The new files as created where it is stated during the export process.
This type of export can alter the quality of the image depending of the option chosen for the type of file , its size, and of course the processing already made.
This kind of export is very similar to publishing.
2) Exportation as new catalog:
This creates a new catalog embedding the files locations and they modifications.
The catalogs are no more synchronized (2)
This does not create new image files unless the "Export negative files"(3) option is checked. Beware that this option seems to be set by default in the export as catalog dialog box.
This cannot modify the quality of an image
Answer to the question
The question seems to mix different concepts "exportation" and "files locations", unless it was implicit that the "Export negative files" option was set.
The move/copy from the cloud to local location is not an export, but can be a operation on the files.
When the files will be on location, you can as indicated above have multi catalogs referring to them. These does not affect the quality of the files as they will be not touched by the duplication of the catalogs.
The catalogs will be unrelated so will need to be very conservative on operation affecting the physical files (moves or any other operation that modify the physical the files).
Unless use of sidecars, processing in one catalog will be independent of processing made in the other one.
But beware, having the same file in two (or more) catalogs is risky.
(1): hpchavaz: Or in XMP side-cars files if the option is set
(2): But if the processing information are embedded in XMP side-cars files, two catalogs can sort of share information on the image processing information
(3) "negative files" means "physical files"