Our app tries to keep the Shopify shopping experience as close as possible to the original experience.
Which means, that the customer will go to your shop, build a Shopping cart just like they usually would, and then, once they're ready to checkout, depending on your settings, they can either have the option to Request A Quote, or be forced to Request A Quote.
This means, that the product physically has to be in the cart in order to be quoted. And if the customer were to click a Request A Quote button on the Product page, then the item will never have been added to the cart, and our app will not be able to register it.
So unfortunately, no, Quick Quote does not support the RAQ button being placed onto the Product Page at this time.