Short answer: No
Long answer: No, because Content Indexing (CI) in Exchange server works in a fundamentally different manner than search folders.
Longest answer: CI works by crawling the store at administrator-specified intervals, creating an index of everything it finds. Then, when you used Advanced Find in Outlook (or Search in OWA), the search will be performed against that index, rather than causing the store to manually look through your mailbox to find the matching items.
Search folders operate on message arrival. As a message is delivered to your mailbox, the server (or client - more on this in a second) goes through all of the search folders and sees if the inbound message matches any of the search criteria on those search folders. If it does, it will deliver the item to the appropriate place in your mailbox (usually the inbox, unless you have a rule that movies it) and put a pointer to that item in the relevant search folders. This comparison for inbound messages happens independently of the CI crawl.
In Outlook 2003, when you're in cached mode and you create a search folder, it will store and activate the search folder on the Outlook client. This helps reduce the load from the server; there are usually spare CPU cycles available on a client machine for this type of processing, whereas on a server, CPU is more of a precious commodity. If you want the search folder to be available to OWA or to Outlook when in online mode, you need to create the search folder from an Outlook 2003 client that is not in cached mode. This causes the search folder to be activated on the server, and so the server will check inbound messages against the search criteria on that search folder.
For more information on how to make search folders available for OWA, see KB# 831400. For more information on troubleshooting search folders, see KB# 831402. In particular, check out the section about how search folders can exist in an active state (bolded) or inactive state (italicized) - you can activate a search folder just by clicking on it, and it will start populating, and as messages arrive in the mailbox after that point, that search folder will be included in the list of search folders the inbound message is compared against.
Number of times I said "Search" above: 21
Number of times I said "Folder" or "Folders" above: 17
And "Search" wins by a nose!