Okay, let me start with explaining the difference between client-side search, and server-side search, and full text indexing ("FTI").
Client side search is available on the Thick Client, and retrieves the requested documents from the server, and performs the actual search using the local PC's CPU & memory. This is often slow for reports that have large-object-support turned on, because the client has to make many (sometimes dozens) of requests against the server for EACH individual document it's searching. The load on the server is relatively low.
Server Side Search sends the search request to the server, and the server itself retrieves the documents to a temporary directory on the server, expands them, and searches the contents for the string provided by the client. This is usually faster than a client side search (because there's no network lag) consumes a LOT of CPU and memory on the server, especially if the user decides to search more than a few files. If someone decided to search 1000 100,000 page documents, the server could be busy for hours.
Full Text Indexing is a separate process that reads each and every document in an application group, and builds an index of every word in the document. When FTI searches are submitted, CMOD hands the query to the FTI server, then waits for it to return a list of documents that contain that phrase.
As for architecture -- again, that's up to you to determine based on how you do things... If your CMOD server has lots of memory & CPU & storage, yes, the FTI can peacefully co-exist on your CMOD server. It might make sense to move FTI to another platform where CPU/Memory/Storage is cheaper (Wintel/Lintel), or expanding capacity is easier (cloud-ish infrastrutcutre / VMs).
Hopefully that clears things up a little.
-JD.