Sure it is possible. Why would it not?
Provided the hardware is compatible, of course; some SATA controllers might pose problems (but not nearly all) etc., but generally laptops aren't an exception.
First try out with a live-cd which you'll find made from Slackware too (some kind at least), and if it runs fine, go ahead. Or you could use any other live-cd to test the hardware first (Knoppix, Ubuntu desktop/live, ...) and if it seems to work, continue installing Slackware; it doesn't differ that much.