In my experience, using deck discard as your primary strategy won't win in T2. However, being able to implement it as a secondary strategy can be very beneficial. Since most of the time, the discard is random the amount it will help you is also random, therefore it really cannot be counted on.
Toss in T2 can definitely be effective since many defenses rely on enhancements with more toughness than strength. Like you point out though, if the opponent has banding options, you're probably better off in a non-toss attack.
Most successful T2 decks do include both drawing and searching, but not all. Some decks might go draw-heavy and use Nazareth to stop the opponent's searching for example. Other decks may go with lots of anti-drawing cards in hopes of creating "dead" cards that the opponent cannot use effectively.
