Yes there is a benefit to being a long-term user of Google Product Search. It will take time to gain traffic for any new website. Data quality plays a roll as well.
One thing to be very aware of is that duplicate content sent by the same seller is prohibited and can cause your products from either site to go offline. Luckily, if your products SKU up on comparison pages, and you are price competitive, it should not take you as long as other sellers with soft goods, or sellers that are not price competitive.
Another factor that will influence your traffic from your new website is that you will have 0 website reviews, so your site will seem not as safe as the other players with reviews.