Well, the actual volume of silicone in three tubes...I'm talking standard 300ml caulking-gun tubes...is enough to adhere and seal that much glass. But when you consider the extra that will squeeze out and end up being wiped off/discarded/wasted...especially if you are new to this wonderful gooey mess of a project

...then I'd say no. Get plenty of extra silicone; it has a very long shelf life, has many other uses in the hobby, and even a partially-used tube, if carefully sealed at the end, will usually still be useful at a later date.
Two more comments. First: Check the best-before date on the tubes you buy. They're good for a couple years, but I have accidentally purchased tubes that were already expired on the store shelf. Didn't notice until after the job was complete, and never had a problem, but why risk it? Buy fresh.
And second: I am guessing that Aqueon silicone...like any other hardware product that is re-branded for aquarium use...is probably stupidly expensive. Just go the the hardware superstore and get clear GE Silicone I; it's been used for this purpose for decades and works beautifully, and will probably be cheaper than the Aqueon-branded stuff (which is likely the identical stuff). Don't get Silicone II. And don't fret when you read on the tube that Silicone I is not for continuous underwater use, or for aquariums. The product hasn't changed, but the labelling has, probably for some obscure liability reason. The product still works as perfectly as it always has. Make sure you have excellent ventilation, as the acetic acid fumes from a larger project can become irritating otherwise.
Take your time, be thorough in removing all old silicone before starting as new silicone won't bond properly to old. Clean the glass thoroughly, have lots of paper towels on hand, and make sure that you have everything ready before you start. Don't sweat it if you get the occasional smudge or dab of silicone in unwanted spots on the glass, it'll be easy to remove with a razor blade after it cures. Once you begin sealing the pieces together, you can't stop for a break; the entire box must be built in one shot, so that there is no point where the silicone begins to cure before you add more.
Good luck!