I would say it depends.
The basic reasoning behind a persistent navigation is to ensure the user can navigate to another section of the site at any time but if your persistent navigation is going to distract the user from making a purchase or distract him from going forward in the conversion funnel, you would be better off focusing his focus on the conversion in mind e.g. clicking on a call to action button rather than using valuable screen space with a persistent navigation. You can also use a persistent anchor scroll on the side to quickly navigate him to the top.
However if the persistent navigation is critical in helping him make a decision then it would be worth having it.
That said, users dont mind scrolling and there are significant research studies that users dont mind using the scrollbar to get back to a point on the page. The quoted text talks about users scrolling to the bottom of the page but I suspect people will be just as willing to scroll back up
Heatmap service provider ClickTale analyzed almost 100.000 pageviews.
The result: people used the scrollbar on 76% of the pages, with 22%
being scrolled all the way to the bottom regardless of the length of
the page. That said, it’s clear that page top is still your most
valuable screen estate.
However you can make it easier for them by providing an option to scroll back up automatically as shown below
Hence my recommendation is to analyze how critical the navigation is to your product page and also do some user tests to see the impact it has on your conversions and then define if a persistent navigation is applicable or not.
I also recommend looking at this article on the pros and cons of infinite scrolling for additional inputs on where it should be used.