... Because you'll most likely end up with an uneven ceiling. The best thing to do, sight-unseen, is to demolish what you have and SCREW right to the ceiling joists. If you're doing this yourself, you'll need some help to hold up the sheets. If you need installation instructions, ask away!
I can't recall ever seeing a 1-inch thick fiberboard ceiling tile. 1/2-inch, yes. You may find the tiles are tongue-and-grove and just stapled in place.
Others may have more to offer. My best to ya and hope this helps.