Short answer: yes. But you have to understand that Pickett's charge was just one piece of a three-pronged assault that Lee seemed to genuinely believe would work. Pickett's charge failed for a whole host of reasons, but for the sake of unpacking this topic in a manageable way, let's break it down into the 3 most important and quantifiable components. 1. The failed coordination of the attack as part of a larger plan on that 3rd day. 2. Hubris. 3. Desperation.

1. Pickett's Charge wasn't the only piece of the Confederate battle plan on the 3rd day of Gettysburg, but rather 1 of 3 components. The Confederate cavalry was supposed to get behind Union lines, but failed to do so in a meaningful way (had they been successful, the Union center might have weakened enough to give Pickett's men a chance...maybe). Also, Ewell was supposed to simultaneously attack Culp's Hill on the Union right, which again, was supposed to pull men and artillery away from the center. Problem is, the attacks weren't coordinated in such a way that would have forced the Union to thin the middle ranks to deal with the other 2 attacks. Ewell got beaten back well before Pickett's men charged, which meant that there was no pressure on the middle to split forces during Pickett's Charge. Similarly, the cavalry attack did not succeed, and the Union center was left intact, and ready to receive the famous charge. Lastly to this point, Lee's artillery bombardment did not have the desired effect, as the slightly higher Union position meant that most of the Confederate shells did not land amongst the northern troops, and failed to drive them off as was hoped. (Which is to say nothing of the very successful Union counter-battery fire) In sum, it was an uncharacteristically bad show for Lee and his generals, who failed to properly coordinate their attack, or take into account the practical realities of the terrain and their opponents.

2. Hubris. This is arguable, but I am of the opinion that modern scholarship is correct in assigning some level of blame to Lee for being a bit too over-confident. This is understandable, as he had defied the odds, and done the seemingly impossible time and again since the Seven Days campaign. He probably felt that his men had done the seemingly impossible before, and if motivated properly, could do it again. Not even Lee was above a little over-confidence, and as the point below illustrates, there were other factors involved that probably fed into this. Still, the record is inescapable - in the year and a half leading up to Gettysburg, Lee had pulled off some amazing feats in battle, and it is fair, I think, to believe that he felt there was at least a chance that his men could do it again if everything went off as planned.

3. Lastly, desperation. Although there was some logic to Lee's notion that the Union center would be weak after the previous day's attacks on the flanks (so, Lee thought reinforcements had been moved from the center to the wings, leaving the center vulnerable), he had gambled on the fight at Gettysburg, was losing, and was trying desperately to recoup his losses. (Like a blackjack player down $200 who doubles down that amount on one final hand to try and salvage the experience.) After all, it was Lee's idea to invade Pennsylvania rather than split his army to send a portion out west to deal with Grant (which was Jefferson Davis' original plan). Lee gambled heavily on this expedition being the key to relieving pressure out west, and maybe even nudging the Union into chaos to the point where a push on D.C. (likely just to threaten) was possible. This expedition was Lee's doing, and by choosing to fight at Gettysburg, he went all in. Disengaging after the 2nd day would have been a failure on a similar level as to what eventually happened anyway, and Lee almost certainly knew that. Sure, he lost a hell of a lot of men by going ahead with his attack on the 3rd day, but the ultimate objective wasn't necessarily to win a battle, but rather to force the Union to weaken their forces in the west to deal with him (and, again, ideally, to route another Union army to further damage northern morale and their willingness to continue the war). This is KEY! Thus, if you look at what Lee had before him at the dawn of that 3rd day, he really didn't have much of a choice: he had to attack. Anything else would have spelled the end of the expedition, and that was going to happen whether he fought or not (so why not fight and roll the dice?).

[Sources - Bruce Catton, 'Glory Road'; James McPherson, 'Battle Cry of Freedom'; Shelby Foote, 'The Civil War, vol. 2'; Douglas Southall Freeman, 'Lee's Lieutenants, vol. 2']