I know the answer: Yes they would absolutely invest in an ecommerce retailer company. They have no "categories" or "types" they avoid religiously.
The filter isn't "ecommerce" but whether it's a "scalable" idea or not.
They might ask "How could you envision your company becoming Really Big in the future?"
Bezos would have said "We're doing books now, but our plan is to be the Wal-Mart of the web".
If you can convincingly argue that your niche businesses in scarves/ties are the gateway to a scalable business you would probably be a good candidate for YC.