I don't know. I haven't read the book (or even heard of it before now) but the premise, that advanced knowledge is forgotten by all but a self chosen few as a consequence of societal collapse, doesn't seem plausible.
But the other aspect, leading the masses out of something resembling anarchy, would still be problematic. There will more than likely be enclaves, lots of them, who would prefer their present circumstances over a return to something more like that which had nearly ruined them.
It would naturally evolve to that over time, but Galt or anyone else coming in and extolling the virtue of shipping the bounty to New York, isn't going to be universally popular in the beginning.
Advanced knowledge was outlawed in Luddite post-nuclear revulsion. (Think contemporary "Green" on steroids.) The monks preserved it, not understanding its significance, in many cases. Leibowitz was an obscure draftsman, who signed many blueprints that were hand-copied as illuminated manuscripts. One such was a drawing for a motor stator, titled "Squirrel cage", which caused no end of bafflement.
One comment I found amusing was a monk wondering why he had to copy a drawing by painstakingly Leaving little white lines to form the image by inking the whole page. it did not make sense.
Over the generations, people began to decode and deduce the scientific and engineering principles, and another civilization slowly rose from the feudal/tribal stages.
In time, this did likewise.
One one of my all-time favorite books. I may need to read it again now.