I think the OP is asking of something is likely to go wrong. The answer is "yes."
You can find the UIDs of your users with the following command:
Find the lines with your users at the beginning (the rest are system "users" that don't log in so much as own and manage stuff) and note the number after the second colon. Mine looks like this for my users:
root should always be user "0", but other users will have different numbers, depending on what the system assigned to them. On some distros the first non-root user always gets UID 1000; others is 500; others are different, still. Even from one PC to the next (with same distro), it can differ somewhat.
The problem is making the UIDs from one PC match those on another so that you can access them from the other PC. Alternatively, you can use a chown or find/chown command to change the UID or user (that is, by name or by number) to one on the other system--either as part of the backup process or as part of accessing the data. I don't recommend using chmod, since this will basically defeat the purpose of keeping the user the same (by setting all the permissions to rwx or some such).
You should look into how rsync deals with user preservation--whether by name or UID. Also look into "--owner", "--group", "--super", "--fake-super", and any others you find in rsync.
Hope that helps.