No.
Hello, I have a question:
Does long range sensors mod improve detection of ships which are using silent running?
Nope. What long range sensor does is merely increase the detection radius of a target, nothing more.
Larger the target (silent running) size, longer the detection radius. Smaller the target size, shorter the detection radius. Of course, if the target in quesion is not silent-running, then it will be detectable up to the max. range of the sensor.
Due to my limited experience in combat, I cannot quantify the min. detection radius vs. silent-running target size relationship.