Since we don't know anything about your website, your business model, your customers, or how small "small" is, it would be impossible for us to advise you on whether it's worth it or not. It would certainly lead to a lot of work, and probably some inconsistencies in the user experience.
One thing you can do to reuse as much as possible between the two would be to use a strict MVC model. The model layer can fetch each piece of data asked for, while the facade layer in front of it can service both kinds of requests.
Let's say your website has a member profile admin page. The model has a Member object with methods for setting/getting identifiers, address, phone number, email address, etc.
Scenario A, JS is enabled:
1) A link from the "profile admin" menu option calls getProfile() on the back end. That builds the HTML/JavaScript to send back by calling getIdentifiers(), getAddress(), getPhone(), etc. and sends that back to the client.
2) The user changes the phone number on their profile page. Since JS is enabled, an AJAX call will be made to setPhone(), and when the results come back, only that portion of the page is updated.
Scenario B, JS is disabled:
1) A link from the "profile admin" menu option calls getProfile() on the back end. The session data will have a boolean noting that JS is disabled, so the page that's rendered has forms and submit buttons.
2) User submits data to setProfile(), containing all the fields, changed or not. What's send back is a re-rendering of the page with the new info via getProfile().
Also see this post about presenting alternate content when JS is turned off.
So it is possible. However, as Bruce said, unless you REALLY need that population, they get what they deserve. I personally would not go through that level of effort, any more than I would try to account for users who might try to access the site through 14.4K modems. All of these tools to turn off JS allow you to specify exception websites.