I wouldn't say that the columns as such were a reason for Napoleon's success. The columns were used because the French revolutionary army had very few experienced officers, as most officers had been nobles who fled or otherwise lost their position during the revolution. Advancing rapidly in columns required much less training than maneuvring around in lines of infantry as most armies did in the 18th century on the Prussian model.

Napoleon just managed to develop a strategy that made optimal use of the columns he happened to have, and exploit inherent weaknesses in the line formations. Most of his victories derive from being in a different place than his opponents expect. In a sense it is true that the columns rather than lines make this possible, as his regiments can move around and turn quicker than the line formations could. But in lesser hands that still might have ended up disastrous, definitely after the shock of the first few victories subsided and the other armies would have been prepared for such a head-on charge as the first columns without Napoleon were.

Before the French Revolution, France was in crisis. She was no longer the main continental power of Europe as Prussia had destroyed them in the Seven Years war with great consistency. So, several within France were looking to reform France's army to ensure that it wouldn't be defeated again. So people like the Comte de Guibert wrote essays on tactics in order to help bring change. Some of these ideas would argue the need for soldiers to fight in battalion over the line.

Experiments were done, and as you have noted, a battalion moving in column formation would be vulnerable to artillery and volley fire. However, a battalion moving in line would take longer to move and have difficulty maneuvering on the battlefield. So movement was decided to stay in line to ensure maximum fire power but movement off the battlefield would continue in line.

Everything changed with the Revolution. When the flight of nobility happened, the army was hit hard (the infantry had the middle of the road amount of losses with about 50% of officers leaving the army, officers at the time were required to have a minimum of two generations of nobility), so the government created a new tactical rule book which advocated a new formation called l'ordre mixte, which I discuss here. This became a standard battle formation during the early years of the Revolution with the idea that regular army companies would be in line formation while the conscripted infantry would be in column formation and use fanatical revolutionary spirit to attack the enemy lines while the regular infantry would hold the line.

From here, we go to Napoleon. Napoleon was famous for not being a creative tactician. We laud him as a genius leader but rarely did he use any concepts that were original to him. Under his command, he would often have his corps commanders use l'ordre mixte but they would often use whatever tactics they decided outside of his direct control. However, the use of the column is also dependent on use of French skirmishers to weaken the enemy lines and also a strong use of artillery to weaken the lines and cavalry to help follow up on the breach that might happen.

The tl;dr is that it isn't a BIG factor but it isn't a small factor. There are a lot of things that contribute to Napoleon's skill on the battlefield and the column isn't the most significant.

They march out of the smoke, and you fire a volley. And the front rank of the column falls, and the next rank steps over them, with drums hammering, and the column smashes your line like a hammer breaking glass... and Napoleon has won another battle. - Sharpe's Eagle, 1993

So, you've got two units of, say, a hundred and fifty men; one is drawn up in three lines of 50, the other is a column ten people wide and fifteen people deep. The column begins to close, the lines fire their rifles by rank - and each volley of 50 has only ten targets (the front rank). Effectively the line unit can kill thirty enemy before the remaining 120 slam into the middle of the line and punch through - and those at the ends of the lines were too far away to engage. (Obviously this is the simple version, but you get the idea.)

As for artillery, they were usually on the flanks of the battle, so their shots would cross the column the "short way".

See Tactics and the Experience of Battle in the Age of Napoleon by Rory Muir, Yale University Press, 2000; pp 82-6.