I agree, it might be a couple of rounds early, but not ridiculously early. Yes, in the second round, that would be a dumb mistake. As an example, the league I'm in, we have two running backs, two wide receivers, a QB, 2 "flex" players (tight end/RB/WR), a kicker, and defense, plus 8 bench players. You definitely want to get your RBs, WRs, and QB set first. But a really good kicker can get you some points, especially if your scoring is set up to allow for bonus points for longer field goals. I've had kickers get me more points than my QB a couple of times, since a 50+ yard field goal is worth 6 points, and a 40+ FG is worth 5 in my league.
And I have my fantasy football app on my phone, so I could definitely finish my draft using it, if something went wrong with my computer.