There's no rule that says you can't look at it before adding it to your hand, and in a practical sense, you usually see it before it's physically in your hand. But, as you said, it would be a nightmare for tracking. It would be easy enough to set it up as part of a specific card's draw, e.g., the way Library works, but to have a particular card be triggered by being drawn, while maintaining tracking, you'd have to make every draw be like Library's, which would be a pain
However, I can actually see a possible card that would work: Suppose you had a card with a reaction like "You may discard [or play] this from a hand of six or more cards ..." Then in that case, the draw from Road Network, or any other source such as Council Room, could trigger an effect