Q: Is it a certainty that WISE would have observed such a planet if it exists?
A: It is likely but not a foregone conclusion that WISE could confirm whether or not Tyche exists. Since WISE surveyed the whole sky once, then covered the entire sky again in two of its infrared bands six months later, WISE would see a change in the apparent position of a large planet body in the Oort cloud over the six-month period. The two bands used in the second sky coverage were designed to identify very small, cold stars (or brown dwarfs) -- which are much like planets larger than Jupiter, as Tyche is hypothesized to be.