Well, consider for a moment the fact that ancient armies (ESPECIALLY Rome) used the tactics that were the most expedient and cost-effective for the time. Yes, I suppose you could offer a few new ideas to the Gauls, but let's look at the drawbacks and why it might not be cost-effective:
You say you want to power this thing using human muscle. But humans tire VERY quickly when working with such heavy weights. This "tank" will have metal plating (very heavy), built out of wood (also very heavy), and each person added to the "engine" mechanism adds their own weight to the machine as well. Then we have to add the ammunition and ballista that make up the weapons.
All of this seems like WAY too much for even the stout barbarians to handle for any length of time (meaning, this thing is going to be SLOW and have a ridiculously short range).
Ballista were effective for their time, but remember the Romans also used them. In fact, almost every ancient society used ballistas to some extent. My point here is that, despite the fact they were widely used, they often didn't turn the tide of the battle. Superior infantry/cavalry and tactics did. The reload rate and accuracy aren't good enough to turn it into any kind of war winning weapon of mass destruction.
Somewhat related to power above, one of the biggest advantages to modern tanks is the fact they can move VERY quickly across even moderately difficult terrain for many miles, especially when accompanied by a supply train of fuel. Without modern fuel and engines, this "tank" is going to be so slow, I doubt it would ever even make it to the battlefield, much less have any impact on a war.
Further, the turn rate and movement speed in battle is going to be absolutely DWARFED by even soldiers on foot. Considering the Romans were very knowledgeable about siege engines, I have no doubt they would quickly find its (many) weaknesses and exploit them fully.
Unless you can come up with a better source of fuel for the engine and make the thing faster, I don't think it will have much of an impact of a war against any faction, much less the Romans.
There is a reason that heavily armored horses/elephants were used as "tanks" in the ancient world. They had the muscle and stamina to carry the heavy loads, while keeping a decided advantage in speed over infantry.