Of course it's possible . Most install images include network support in their kernels. It would be a fairly trivial matter to add an SSH server and set it up to auto-start networking.
The swapping HDD method is probably easier though. Just make sure the disk is in the same place it will be in the destination machine (primary master disk, probably), or you'll probably run into problems.
I don't know what the state of Slackware's hardware detection is these days, but it's probably nonexistant. Recognize this when you're adding modules to load.