Yes, if you take care of the SEO, implement a little of server rendering, and have all the things that make de SPA a little tricky i don't see the problem. All the things like the shopping cart, or other things that are more complex in plain jQuery, with SPA becomes more easy and you only need a robust API that maybe Firebase can help you :)
If you would like your users to be engaged in your app and want them to stay in your site for a while, you might not want to build an ecommerce as SPAs. In my opinion, most of the e-commerce website visitors today are used to huge amount of pages and therefore would be comfortable looking at the websites that give them an illusion that they are in the real shopping mode. Most of the users on these websites are just ordinary people trying to buy or look at the products that you have and for them, more than the website itself , price is important. For example, look at Amazon , I don't think they care much about the UI or how the button looks on their websites. But still they are able to capture what people are thinking about when they visit amazon websites. This might be funny but at one point I was shopping in Amazon so hard that I had at least 50-60 tabs open with varieties of items on each page.
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stuff ;)
well if you read up on SEO with singlepage apps first and build it accordingly it should work.
just take those factors into account. maybe pick isomorphic rendering so the first payload delivered for an specific uri is already a rendered markup that will be bootstrapped. So it should be react or angular2 or something that actually supports this technique :)