Depends on the champion for whether or not KDA matters, and obviously it will matter if it gets too bad. I'm talking about if you feed a couple of early kills, but then play safe and farm up.
For example, on late game hypercarries or on tanks, they'll scale into the late game no matter what. If you can sit back, farm, and try to avoid fighting them 5v5, you can come back from nearly anything as a tank or a hypercarry. On the other hand, if you're not doing so well as one of those but your teammates are, you can teamfight and just take assists to help you get back in and try to stay safe.
One game, as Twitch, I lost lane pretty hard, but I still came back in and tried to carry (that game, my Brand mid was inting. In Ranked. Literally running down mid).
Other champions, however, do care about KDA a lot. Anyone who is reliant on an early snowball does care about KDA a lot because, if they don't get it, they're probably going to start to fall behind and, if you start to feed, you just become useless. Riven is a good example of this. As Riven, if you're even, you're behind, and if you're ahead, you're unstoppable.