No, the creation of the Silmarils would not have marred the Two Trees in this way. The light of the trees is not a limited resource, and pieces of the trees continued to radiate eternally even after they were separated from the trees themselves. From the dew that dripped from the white tree Telperion, Varda made the stars that gave Middle-Earth its first lasting light since the fall of the Lamps. Even after the Two Trees were killed by Morgoth and Ungoliant, a single flower from Telperion and a fruit from Laurelin were still eternally alight and could be set in the sky as the sun and the moon. However, these secondary lights, although never diminishing, were qualitatively inferior to the direct illumination of the Two Trees.
What was remarkable about the Silmarils was that they preserved the ever-glowing light of the Two Trees with all its original qualities undiluted. (How Fëanor managed to accomplish this, he refused to say.) In fact, rather than diminishing the original Two Trees, the Silmarils preserved their light so that the trees can eventually be recreated. The form of the trees could be recreated by Yavanna, as she made Galathilion, as a copy of Telperion, but the copy that cast no light; the light of the Two Trees could not be recreated, even from the moon and sun. However, after the Dagor Dagorath (the final "Battle of Battles" against Morgoth), when the three gems are recovered from the sky, sea, and earth, Fëanor will repent his crimes and, released from the Halls of Mandos, he will finally reveal how the Silmarils were made. With this knowledge, the gems may be broken open, to reveal the pure light of the Two Trees stored within, and with this light, the Two Trees may be recreated with all their original brilliance.