Hi Catherine..
Yep..Auctiva works wonderfully with a store.
I have 500+ items in my store and Auctiva worked flawlessly uploading those listings into my eBay store.
Someone else will be along to answer how they work together...
What I like is how they work independently from one another. More links for search engines to pick up. Another link to place for buyers to find items, etc.
My Best,
Donna