It appears from the description you have several servers each with a cable to a switch in the server room. What speed those connections are is the main thing to look at.

If a room with it's own switch does transactions mainly with just one of the servers, performance isn't going to be improved (and cabling costs will be greatly increased) by wiring directly to the switch the servers are on - unless the server connection to that switch is a gigabit or 10-gigabit connection and the cable run to the server room is 100-Mbs.

If the rooms do heavy access to multiple servers (or if the server connection at it's switch is 1-Gigabit or higher), then separate cables to the switch the servers are on will be faster, depending on traffic density.

If the switch serving the room connections is peripheral, NOT the one the servers go to, then you're back to the single cable situation you have now - no difference whatever except much higher cabling cost - unless the server switch is a gigabit switch and the connections to the peripheral servers are gigabit connections - then it would be faster than 100-Mbs connections to the room switches.

If the traffic density is low, it doesn't make one bit of difference how you do it, but if you're doing intense work against an Oracle server or something like that optimization is worthwhile.

Even so, I'd recommend local switches with a single gigabit connection each back to a gigabit switch at the servers to minimize cabling expense - but if the server room peripheral switches aren't gigabit to the server switch and servers, you're just spinning your wheels to do anything different.

Cabling is expensive and difficult to move around for M&A (moves and adds), so you don't want to incur cable expense unless it's really worthwhile.

Switches separate the traffic so each port sees only it's own traffic, not all traffic as with hubs (switches are just fast multi-port bridges).

If you have a gigabit leg between a server and a switch, that cable pools all traffic coming from all legs to that switch. If your switch had 10 100-Meg ports and one gigabit port to the server (which must, of course, have a gigabit card), you'd have to saturate all 10 100-Mbs ports with traffic for that server to saturate the gigabit leg, If the leg to the server is 100-Mbs it will be easily saturated and the legs out of the switch will be unable to achieve anything near 100-Mbs because there's a bottleneck at the server.

If you have peripheral switches feeding into a main switch with the servers on it, the legs to the peripheral switches must be gigabit also or you have serious bottlenecks between the switches.

My default would be a gigabit switch with the servers and peripheral switches connected to it all through gigabit ports, and the peripheral switches would have 100-Mbs ports facing the workstations. Of course, I'd try to push those peripheral switches out to the workgroups if possible to cut down the cost of pulling cable.

If all your switches are 100-Mbs on all ports, including the server ports, rewiring is highly unlikely to give you much of a performance boost.