Yes but you'd need to physically move the drive from PC to PC unless you
1) plug in the drive to one PC and share it on the network
2) buy an external drive that has NAS capabilities like a Buffalo Linkstation
0r 3) buy a Linksys NSLU2 NAS adapter
Any of these options will allow you to see the external drive as a network drive so you could back up any PC to it but my recomendation is to get a all in one like the linkstations if you haven't already purchased the external hard drive. If you have got it the Linksys unit is pretty neat as it can be hacked to do all sorts of jobs (iTunes server etc.)
An external USB drive can be connected to the desktop and then you can mount that drive over the network to the laptop. Add Acronis True Image disk imaging software to that and you can do backups to that drive for both machines.
If images aren't necessary, a program like Viceversa Pro will allow copying files while keeping track of what files are new and what are changed; you can also do mirroring if you have a folder with files and periodically want to sync that out to the external drive (I do that with my MP3's to make sure I have a second copy of them in case of a harddrive crash.)
The above should be very affordable solutions that work well. Of course, getting some Network Attached Storage (NAS) gear will work at least as well and be independent of both computers, but might cost a tad more.