It could very well... Lets put it straight.
If the person had already used synthetic and the dealer put in conventional oil, that already could mess it up. The bearings would have already been saturated with synthetic and the mix of conventional oil will either resist mixing or break down (synthetic breaks down conventional in this theory) depending on what theory you prefer. Either way, the result is the same and the damage could or could not have been done. The damage would be overstressed bearings since they don't get the proper lubercation. I don't see it as a huge deal as long as you stick with the product you want to use. Don't change back and forth!! The bearings will eventually be saturated in the oil you use, even if it takes 3k more miles and another oil change.
On the other hand, if the car's been 100% conventional, then the risks are leakage. Synthetic not only is a lot thinner (molecule wise) than conventional oil, it also is great at breaking down sludge in your engine. However... if damage has been done to oil rings.. then synthetic could slip past and start leaking. On an even worse case, that sludge sometimes keeps everything from leaking in the engine. Imagine filling a bike tire up with fixaflat, and poking tiny holes everywhere with a needle. Sure, it won't leak, and if it does, you probably won't notice, but then imagine adding something into the tire that cleans up that gunk fixaflat has in it... ya, oh crap is right. Synthetic oil acts as a decent gunk remover.
Don't take what I've wrote 100% to heart. I just read a lot and most of my information comes from the Internet and car-enthused friends, so I could be inaccurate in some respects if not all. But, I also come up with my own conclusions on what I think would happen. My credibility only relies on that I'm a student engineer and I'm a co-op at Toyota at one of their automatic transmissions and engine plants.