If by category id you mean the mysql internal id number, no. If you are moving your store, it will be much easier to use the Backup MySQL database contrib, or your host's phpMyAdmin through the control panel.
Basically, you set up the store in the new location but without data. Open the SQL backup and remove any server specific settings. Usually best to redo payment modules by manually entering them.
I don't know if there is an FAQ on moving a store, but it isn't that hard. If you set the store up in the same way, you can use almost certainly use the backup contrib to restore your data at the new site.
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