However, the regular Animorphs can only use it when they are in morph.
Except Tobias, who can do it in Hawk, his base form. And also in his human morph, though I'm not certain if they ever showed him doing so.
Tobias' condition is an anomaly in itself. Nobody has ever gotten their morphing powers back after turning into a Nothlit, so things are bound to be different for him. I'd guess that the reason why he can use thought-speak in his 'natural' hawk form is that it was originally a morph, and because he ended up staying that way, he can always use it like Ax, in an out of morph.
Because of this, Tobias should technically also be able to use thought-speak when he morphs a human, but for some reason K.A never went any further with this. It seems like she changed her mind on a lot of things and had a hard time keeping track of everything (who could blame her?)