In my experience, a chat window shouldn't be shown by default. There should be a button they can click to engage in the chat. At this point, I think it's mostly opinion, but I chat should appear in page. The exception is if the chat is likely to take place across several pages, then a popup might be more beneficial in that case. In general though I find people hate popup windows and prefer things to stay on page.
As to your idea of showing a chat window after a certain amount of time, I'd default to no. However, if you feel that time spent on page is a good indicator of needing help, which good testing should be able to tell you, then maybe highlighting the chat button or displaying a non intrusive message asking if they need help would be better than just opening a chat window.
Finally, something to consider given that you have an e-commerce site is that real estate is prime for your page. That screen space could better serve you displaying product instead of a chat window. Because of this I would limit the chat window as much as possible and only bring it into play when the user wants to use it.