Airport Extreme and Portable Hard Drives

In theory it should, just try and see; worst case scenario Time Machine won't recognize your old backups, but won't touch it if it happen.

 

The on-disk storage method when performing a Time Machine backup over the network (sparsebundle) compared to directly connected (hard-linked directories) isn't the same. You can bring the USB drive along, but the backups you make won't be visible between the two methods.

Even worse, you will get two copies of your data. One copy using the wireless method, one copy using the direct-connect method.

 

The usual way to restore a TM backup is with the Migration Wizard. I don't know if the migration wizard can recognize a sparsebundle on the disk and pull information out of it. That would be easiest for a full restore.

If you just want to pull files out of the backups, then I think you can double-click on the sparsebundle file and "mount" it. Then you can pull files off of the contents. A sparebundle file is kinda like a disk image, it's just laid out differently on the disk.