Yes, but not at the same time unless you have two licenses.
I want to be able to start a project on my laptop then work on it in my pc. How can I do that?
Read Bill Hunt on project setup http://forums.adobe.com/thread/919388?tstart=0
If you do the above on a FAST external (eSata or USB3) you will be able to move the drive from one computer to another
With TWO notices...
1-You will need to LOCK the drive letter in BOTH computers so you are not constantly having to relink files
2-Be prepared to RE-conform the files every time you move from one computer to another
Search http://search.microsoft.com/search.aspx?mkt=en-US&setlang=en-US to learn how to lock an external drive letter
Read Bill Hunt on Conforming http://forums.adobe.com/thread/726693
For migrating Projects via external HDD's, this Tips & Tricks article might be useful too: http://forums.adobe.com/message/5880839#5880839
I migrate from my laptop to my workstation often, and use external FireWire-800 (IEEE-1394b) units, with no issues - once the drive letter for the external has been set to the same, in the OS of both computers.
So I guess a trip to Best Buy is in order for a FireWire?
Well, if you have eSATA, or USB 3.0, there would be no need for FireWire 800 (IEEE-1394b). Those two connections will be faster, and nearly as fast as working off of a 7200RPM internal HDD.
If you are buying external HDD's, whether FW-800, USB 3.0, or eSATA, I strongly recommend that the discs be 7200 RPM (minimum), as 5400 RPM discs create playability issues.
Also, you will want to make sure that for a PC, the externals are formatted to NTSF, because FAT32 has a file size limit of ~ 4GB, and that can present problems.