Or would I need to make some modifications to the HDD to get it to fit or work with the laptop?
Really depends on the type of connecter your laptop is using. Typically newer Laptops use SATA or m-sata connector so the hard-drives in the i-pod classic cannot directly be used in a laptop as the hard-drive in the ipod classic use a zif-connector (flat ribbon cable type).
Sata (2.5") and M-sata (typical for newer 1.8"):
Older 1.8" Laptops might use micro-sata or even Zif-connector. With the exception of an zif-connector you probably will need some type of of adapter. But generally speaking you can use the ipod harddrive in a regular laptop depending on you having the right adapter/connection in the laptop.(Example of an adapter)
1.8" micro-sata connector:
1.8" Zif connector:
If the laptop takes 1.8" drives then yeah. I don't know where you would get one though. Smallest HDD I have seen in a laptop is 2.5"
You could buy some sort of adapter to get it to fit in a conventional laptop drive bay.