I'm waiting for the tile store expert to post but the pros use long handled scrapers to get glued carpet up. Work is never fun. I would go ahead and take up the old tile to avoid a double layer but at least inspect it cause cracks in it may cause cracks above.
Either way, the thinset with at least a 1/4" notched trowel is forgiving and workable and will make up for minor differences in level, pits, and shallow glue remains. Vinyl of course is a different story.