Hello! You are correct: on the studio version of 2+2=5, Thom uses two pedals in order to get two different tones: one for the “paying attention” section, and a second for the song’s final section. You can actually see Thom turn on his BOSS CS3, then deactivate his ProCo Turbo Rat in this video from the recording of 2+2=5 at Ocean Way Hollywood Studio B (now United Recording Studio B). After the band stops playing, Thom leans over and lowers the volume knob on the CS3. You can even hear the characteristic “clink” of the BOSS enclosure when Thom switches on the CS3. Given that the band recorded 2+2=5 in only two hours, it’s highly likely that those pedals made it onto the final version of the track, with the CS3 pushing Thom’s AC30 for a bright and punchy clean-ish sound and the Turbo Rat used for his heavier distortion tone.
In live performance, Thom has played it a little differently over the years. For example, at the 2003 Letterman performance, rather than bring his full pedalboard to perform a single song, Thom used a single Turbo Rat for the heavier distortion tone and simply used his amp for the clean-ish tone. You can see Thom deactivate the Turbo Rat as he sings “attention” for the last time in the Letterman video. He uses the pedal intermittently during the song’s final section as well, turning it on and off to highlight each repeat of “but I’m not” (or “cause I’m not” or “maybe not”).
On more recent performances of the song, Thom has used his Crowther Hotcake for his heavy distortion tone, and likely uses his Telenordia TK-23 Kompressor for his clean-ish tone.
A screenshot of Thom stomping on his ProCo Turbo Rat during the September 2002 recording of 2+2=5 at Ocean Way Studio B (youtube).
A screenshot of Thom stomping on his ProCo Turbo Rat during the 2003 Letterman performance of 2+2=5 (youtube).