Yes and no. Your toilet will operate similar the flush toilet at home, but you must NOT leave the toilet's drain valve open. If you do, the liquids in the waste will immediately drain off, leaving the solids stranded on the floor of the tank. The solids then harden into what is called "the black cone", a hard mass which is very difficult to remove. A better idea is to let the waste, both liquid and solid, accumulate in the black tank. Then, when the tank gets near full and you open the drain valve, the whole thing empties with one big "whoosh", leaving a more-or-less clean tank. In fact, when dump time arrives, it is a good idea to fill the black tank with extra water, to increase the force of the "whoosh".
. . Some folks avoid the black cone by never adding solids to the tank, preferring to use the campground outhouses/toilets. Nothing wrong with that, but it seems to defeat the reason for having a toilet in the first place.
. . As an added note, after you drain the black tank, it is a good idea to immediately drain the gray tank right behind it. The water from the gray tank cleans out the dump hose and fittings.