It's possible, but you would need to use a Type I Combo Preamp with the Leslie 147. Leslies are designed to take hot, speaker level input, so the line level signals from the Tyros would not be sufficient. (Some of the later solid state models might accept it - just)
You wouldn't want to use a 122. For all its 'Holy Grail' status amongst the 'It must be a B-3 plus 122' people, I don't rate it as highly as the 147. Less treble, harder to hook up (needs a balanced, speaker or Hammond pre-amp level input) and there's an annoying delay when you switch speeds. And there's a premium to pay for the 'superior' (not) qualities of the 122.
I'd be inclined to look for a 760 or 770. Solid state, more oomph and cheaper. You'd need a Type II Combo Preamp. People will rightly say that it doesn't have the warmth of a 147 but, having tried them side by side, at normal volume levels there's precious little in it. If you want that tube overdrive at low levels, just use one of the DSP effects in the Tyros before the signal gets fed to the Leslie.
Of course, all the sounds will spin, including pianos, strings, rhythms etc - unless there's a way of routing just the Organ Flutes through the Leslie.