Rally mode in itself does not change throttle response, engine characteristics or abs behavior.
What it does is let you choose throttle response between offroad, street or (stupidly) "Rally" on the 790 which creates alot of confusion. The drive mode and the throttle response are two separate settings so why name them the same?
You can also set abs to street with abs on both front and rear, or off-road which disables abs on the rear wheel. On the 790 there is also abs off, an option the 890 doesn't have.
The big thing with Rally mode is the adjustable traction control (MTC) which you can adjust in 9 steps while riding, using the up and down buttons on the left control above the blinker button.
All these settings are remembered if you leave rally mode and then activates it again later, sparing you the hassle of changing a bunch of settings as soon as you leave the pavement.
Now, some other things, like cornering abs and wheelie control stuff can change their characteristics or turn off depending on abs and mtc settings, but are not directly linked to the bike being in rally mode or not.
#2