Does this result in noticeable input latency that you can feel through gaming, similar to the sort of input drifting feeling you get with wireless peripherals?
No. According to the USB spec, maximum allowed round-trip latency to any peripheral (regardless of the number of hubs) is 1.5 microseconds, many orders of magnitude below what a human being could sense. Electricity will propagate over a 32' cable in around 50ns, another couple orders of magnitude smaller still.
Also, do you use hubs on the end for the keyboard/mouse or do you run a separate cable for each one? If you use hubs, have you run into issues with using them? Do you have gaming quality peripherals on the end as well (high dpi and polling mice and high poll rate keyboards)?
I have a hub attached to each one, with a cheap keyboard and a Logitech MX518 mouse. Guests are welcome to bring their own peripherals if they so choose.
I ask as gaming peripherals tend to put more strain on USB connections then normal peripherals and can crap them out when they're operating on the edge (like the 32' repeater you mentioned). They draw more power and operate close to limitations of the spec in terms of latency.
The hubs are powered. They are USB 2.0, so they support many orders of magnitude more bandwidth than you could ever generate with a keyboard or mouse.
With all due respect, I think you're been fooled into believing the marketing of some companies that want to sell you expensive placebos. Keyboards are just not a significant source of latency in any gaming setup.