As far as I am aware, the latest spectral types that have been assigned are around Y2, for objects like WISE 0855-0714 that have temperatures around 250 K or so. I've also seen several directly-imaged exoplanets have had their spectra classified as L- or T-type (e.g. Bonnefoy et al. 2016 who find that the giant planets HR 8799 d and e are good matches for L6–L8 dwarfs).
Jupiter is colder and less massive than the observed Y dwarfs and differs from isolated brown dwarfs because it is being illuminated by the Sun, but there is thermal emission which could be observed from the nightside of the planet. Has Jupiter's nightside spectrum (i.e. the spectrum of Jupiter excluding contributions from reflected sunlight) been observed in sufficient detail to compare it to the spectra of Y dwarfs, and if so does it fit the trends observed in spectral type Y or is it so different that it cannot be spectrally classified as a Y dwarf?
For clarity: I am asking purely in terms of spectral classification, i.e. the classification of the spectrum. I am not asking about whether Jupiter is a brown dwarf making the Sun+Jupiter a binary system. That has been asked elsewhere.