Little Wars is not by any stretch of the imagination likely to constitute a watertight ruleset (give it a break, it was the first of its kind!) so I think we have to apply a bit of common sense to ruling on this issue. I quote from the text:
Moreover, in our desire to bring the game to a climax, we decided that
instead of a fight to a finish we would fight to some determined
point, and we found very good sport in supposing that the arrival of
three men of one force upon the back line of the opponent's side of
the country was of such strategic importance as to determine the
battle. But this form of battle we have since largely abandoned in
favour of the old fight to a finish again. We found it led to one type
of battle only, a massed rush at the antagonist's line, and that our
arrangements of time-limits and capture and so forth had eliminated
most of the concluding drag upon the game.
This seems to indicate that "three men on the back line" constitutes something of "strategic importance". In my mind, this suggests that the three soldiers have struggled through the enemy defences to capture the opposing HQ, or something of that sort. It's hard to see three men reaching the back line only to be shot down as constituting that sort of victory.
So I'd definitely be inclined to think that you have to have three men reach the back line alive to reasonably "capture the enemy flag", or whatever else such a victory condition is meant to represent. What's the alternative? That covering the distance of the battlefield is in and of itself a victory condition? That doesn't sound much like a "Little War" - more like some kind of running race :)