Yes, you can access the drive...
You need an adapter to make all components fit the cables system in the new unit.
What we prefer to do is to insert the laptop drive into an external USB enclosure... then plug it into the new computer's USB port. After a short adjustment, your new system will give the laptop drive an ID, such as E, J or whatever... then you can go look at anything on the drive... copy files, and so on.
There is more to the install, if you want the laptop drive to work as the main drive in the desktop, but it is possible to do that, as well, by running the Windows Disk that setup the laptop drive in repair mode... to set it up in the desktop... then adding drivers and such.