Yes, but question..
Is the goal to simply access for more OR do you want the hard drive to be portable and move wherever you take your laptop?
You can access the Desktop's hard drive over the network if both of them are connected to a router - like many people have to share their internet connection between 2 PCs.
To do this, designate a folder which you want to "share" on the Desktop..
Right click and choose "Properties"
Click on the Sharing tab and choose to share the folder.
Click on the permissions button and make sure "everyone" has modify rights.
Click on the Security tab and make sure at least 1 user has "full control" of the folder.
Click OK
VOILA! the folder on your desktop is shared over the network.
NOW, just go to the Laptop and Click on Start then Run and type in \\desktopcomputername and hit ENTER.
BAM! You are accessing your desktop computer's hard drive over the network. You can copy and paste files, listen to music, watch movies, etc. over the network.
OR, to make it portable. -- buy an external enclosure which will enable your hard drive to be plugged in via a USB port on the laptop. THEN remove the desktop hard drive and insert it into the enclosure. You can then take your desktop hard drive wherever you want.
Try an external enclosure from HERE: http://www.newegg.com/Product/ProductLis...
Just make sure you know if your desktop hard drive uses IDE (PATA) or Serial (SATA) and make sure the external enclosure has that type of connector.