This is sort of a cautionary lesson to those thinking about trying this, especially those who don't already sell on Amazon. Certain types of stores just aren't a good fit. My store carries mainly limited items and one-offs from overseas brands; we might only have one or two of each item in stock, and we're just constantly adding new items as we sell what we have.
First, signing up for an Amazon Professional Seller account is time-consuming in itself, and it also costs $39. There's no real way to "try out" the Amazon channel before paying that. So you could be out of luck if you figure out it's just not for you.
Because our products were not known to Amazon, I had to fill out a bunch of new info for *each* product. Amazon also has its own image requirements (that Amazon itself doesn't follow), so if you're given images from the manufacturer that aren't 1,000 pixels on one side, you basically can't list an item.
In the end it was clear that it was going to be at the very least a huge amount of work to get my listings on Amazon, and that the time I'd take doing so would be better spent just trying to sell them on my own site, especially considering we only have one or two of each item.
Also, if you sell on Amazon, be aware that you have to abide by their liberal return policies. Since our items are imported, mostly handmade and limited (and also since we have so many people asking us to "borrow" our items), we have a strict return policy and our customers all know it. The Amazon return policy alone was almost a dealbreaker for us.
I guess I expected this to be more of a Shopify sales channel like any other - your products and inventory are still in Shopify and your store policies apply. But this is really just like a sync app between two totally separate stores; one your Shopify store, the other your Amazon store. If you already sell on Amazon or you have a store that's only got a few products but many of them (rather than the reverse), then this might be a good fit. It wasn't for our store.