I have not used slate tile, though I did keep some juvies for awhile in an old fashioned slate bottomed 5 gallon aquarium. I wouldn't think you'd need to seal it.
I use slate tile and I have never sealed it. To clean it I soak it in water and vinegar, then I wipe it down. Rinse it with water and hit it with the heat gun to dry it quickly, wait for it to cool then stick it back in the tank.