Perhaps. Lee's logistical situation in general in that campaign was full of more holes than a slice of swiss cheese as of that campaign.
He had somewhere around at most sixty thousand men when he decided to march North.
He had forty thousand odd at Antietam. Not counting one brigade of under a thousand men (perhaps six hundred) at Harper's Ferry and artillery (perhaps six batteries, tops).
It is possible that he would have fifty thousand with good shoes, but given how bad the supply of food was...I don't think so.
I'm sure it would help. I just don't see it being enough to change things meaningfully.
The huge perk of better shoes is that that problem being solved frees up energy and trains and so on to handle the rest. That might lead to a meaningful boost.
Regarding the idea that the "human foot is ideally suited to walking"...I'll just put it this way. We invented shoes for a reason. I'm reasonably sure it was a good one.
Addition:
According to
http://www.tngennet.org/civilwar/tncwindex.html these four regiments of Bushrod R. Johnston's brigade had a not inconsiderable number of men sent to the rear prio to the battle.
17th Tennessee: 371 men. The barefoot men (122 in number) were sent to the rear, thusly leaving only 249.
23rd Tennessee: 207 men. 26 barefoot men sent to the rear.
25th Tennessee: 145 men. No mention of barefoot men sent to the rear.
44th Tenneseee: 350 men. 56 barefoot men sent to the rear.
That means that out of 1073 men, 204 were sent to the rear. Nineteen percent of the brigade's strength. I do not know if this was typical, but if it was, this would mean all the men in his army having good shoes would add a considerable number of men to Bragg's army.