The short answer is, yes Napoleonic era troops would actually do this. Overcoming an enemy in a defensive position meant applying maximum force at the same time. Hopefully, tactics would be used: charging against a weaker place like an unsecured flank, or after their own artillery had had an effect on that opposing battery. Or, if there was a real fort with strong internal lines of supply and defense, the attacking army might opt for a siege, dig trenches. But we're talking about combat being manual labor, here, so if there was an assault on a defended enemy position the most possible soldiers would have to arrive at the enemy lines at the same time, to have the most impact. And that means a line of them, or lines. Running might seem a good idea, but it tended to break up the line- some would arrive before others, and so there would be less impact: it's much easier to defend against a piecemeal attack, if attacking soldiers are straggling in.

However, the way to actually get soldiers from place to place quickly was to march them in a column. Napoleon sometimes would get his soldiers out onto the field in columns. There has been a controversy in the past about when and whether he intended to fight in columns, or tried to form up his troops into lines from columns after they'd come pretty far forward- maybe somebody better informed can weigh in on that debate, but if they don't here's something more on it. But the old notion about him fighting columns against lines seems to be at least far too simple, perhaps is untrue.

As far as getting smashed up by artillery, however, you are right to suspect that it wasn't popular with the troops. Wellington was known for sometimes defending by putting his main army just beyond the crest of a hill, opposite the French artillery, leaving lighter forces on top, and even letting them lay low. This made those troops rather hard to shell. Use of a reverse-slope was effective and annoying to the French in the Peninsular Campaign and at Waterloo, and would also annoy them greatly when it was used against them again, around 150 years later, at Dien Bien Phu