Pioneer 10 was about 80 AU when contact was lost in 2003 and both Voyager 1 and 2 traveled more than 100 AU and they are still operating. This put those 3 probes for years in the range of Kuiper belt and even close to orbital aphelion on an SDO. I know that those 2 zones are pretty rarefied, the possibility of a close encounter is minimal and no gravitational deviations beside the Pioneer anomaly were observed. My question: one of the instruments on board of these probes could have detect an object, in case of a distant encounter?
The list you linked to, shows that the instruments that are still active, are meant for the detection of solar wind and cosmic rays. The magnetometer could be useful, but a planet needs a liquid core to generate a magnetic field. It is unlikely that any KBO is warm enough to have a liquid core (or we'd be able to detect it using IR telescopes).
What's left is optical detection using the camera system. This has been switched off for years. It's unlikely the probe has enough power available to use it. Even if it did, the camera probably broke when its heaters were switched off.
Also, the camera system was built for imaging nearby planets. It's 1970s technology that probably doesn't have enough resolution and sensitivity to search for dark, far-away objects. Another problem would be data transmission: to do a thorough search, you need lots of images. To transmit these at high speed (115 kbit/s), NASA needs to allocate a 70 m DSN antenna.
There is one way these spacecraft could contribute to KBO detection: a big enough course deviation due to gravity of a nearby KBO would be detectable from Earth.
There is some evidence this already happened once. With only the course deviation to go on, they haven't been able to define the size or orbit of this KBO, though.