It is possible.
The clearest way to go about it, providing true numbers is to simulate a client that performs some sort of activity that mimics the real usage. Then have that client periodically use the website.
This presupposes that your website has a means to accept inputs that do not impact the real back end business. Crafting such interfaces requires some thought, but is not beyond the ability of a person who could put together the web site in the first place. The key points are to attempt to emulate as much using the real website as possible, but guard against real business impact. Basically it is designing for a special user (the tester).
So you might have a special user that when logged in, all purchases are bound to a special account that actually is filtered out to appropriately not demand payment and not ship goods. Provided the systems you integrate with all share an understanding of this live testing account, you can simultaneously test alongside of real production post-deployment.
Such a structure provides a huge benefit. You get performance of the real, live running system. Performance tends to change over time, and is subject to the environment. By fetching your performance numbers on the live system, in the same environment, you get a much better view of what real users might be encountering. Also, you can differentiate and track performance for different activities.
Yes, it is a lot more to design and set up; however, if you are in it for the long run, the benefits are huge.