Counterfactuals are always difficult, but in this case I am sure that the answer is somewhere between "no" and "after years of hard work". Certainly it wouldn't have happened overnight -- whereas with psychedelics it very literally did happen overnight. Even if the psychedelics were simply a shortcut, there was a lot of benefit in taking them: within a year of my trip I'd completed 15 credits worth of maths courses, and the rest of my education and career benefited accordingly. I'd been trying for years to overcome those anxiety issues organically and was still only a fraction of the way there, so the non-psychedelic path would not have yielded results in time to benefit me in university.