Does anything placed at the Lagrangian point L1 between the Earth and Sun obscure the Sun like a transit of the innermore planets? The James Webb telescope is to be placed at L2, but if it was placed at L1, would it be in front of the Sun when looked upon from Earth? When you looked from the equator into the Sun, the telescope would be in the very center of the solar disc, right?
Objects are not place at the Sun-Earth L1 or L2 Lagrange points. They are instead placed in pseudo orbits about these points. These pseudo orbits intentionally avoid being directly in line with the Earth and the Sun for two key reasons. One reason is that these points are directly in the line between the Sun and the Earth. An object at the Sun-Earth L1 would be hard to see, while an object at the Sun-Earth L2 point would be in the Earth's umbral shadow.
A much more important reason is the incredible amount of propellant that would be needed to maintain their position at those unstable Lagrange points. The pseudo orbits, while also unstable, are much less unstable and require considerably less propellant for stationkeeping.