Is it ever revealed how many beings died during the Time War?
No. There are only hints as to the incomprehensible scale.
It effected multiple civilizations across multiple galaxies. Neither side hesitate in actions that caused collateral damage.
"...you aren't finished yet! Some of the universe is still standing"
Pilot Cass to a "Time Lord" re the War - "The Night of the Doctor"
It effected multiple timelines as both races had access to time travel and would race back through time to alter future events to their advantage.
This is the kind of war that featured horrors such as the "Could've Been King with his Army of Meanwhiles and Neverweres"
"At the heart of the war, millions were killed and brought back to
life every second." (see "The End of Time")
The only weapon the Time Lords hesitated to use was the "Moment", a weapon that could judge them (and then wipe them out). (see "The Day of the Doctor")
The Time Lord's leader, Rassilion, attempted to win the war by creating a paradox so severe (The "Ultimate Sanction") it would destroy the entire space-time vortex (and the universe). The Time Lords planned to escape the destruction by transforming to become entities of consciousness alone.
(see "The End of Time")
The Dalek's attempted (and succeeded in one time line, see "Turn Left", thanks to the 'Trickster' -
'Oh my God, Donna look, the stars are goin out' - Wilfred Mott
) to detonate a "Reality Bomb" to wipe out everything except themselves not only in their current universe but also in all parallel universes. (see "Journey's End")
So, depending on your temporal philosophy, if you think lives lost in other time-lines and parallel universes count as fatalities, the total fatalities from the Time War is in the order of "nearly everyone ever anywhere"
for more background see