I've seen this functionality built into a Geocortex web app. It's an invaluable tools as TOC layer list's can get lengthy depending on the purpose of the app. Often you may have related data layer representing different time periods or geographies or the app is simply meant to catalog data, in such cases it becomes difficult to dig through or locate all related layers.
Does the search tool that appears next to the layer list by default do what you're after? It filters the list of layers shown below as you type.