The primary issue I can see is that insect antennae aren't a body covering in the same way that mammalian hair, reptile/fish scales, or bird feathers are. They're a distinct pair of legs that have been twisted and modified into a pair of sensory organs, in the same way that four pairs of legs have been crammed into the head to form the maxillae, mandibles, labrum, and labium.
The way insects and other arthropods work is their body is divided into a number of segments, each of which has a pair of legs. You can fuse and compress segments together (making the thorax and the head in insects, or the "two sets of legs per segment" seen in millipedes), have multiple legs doing the same job (crustaceans have two pairs of antennae), but insects never really get around the "one segment per set of legs thing". To make an insect with antennae "hair" you would have to duplicate the segments many thousands of times so you have 60,000+ segments in the head alone.
It might be better to just have chemosensory setae (olfactory "hairs" that cover the entire back of the head) that evolved as a secondary sensory organ to help the antennae. Almost all insects have setae and in many species it can make them quite fuzzy (bees, moths, velvet ants). Though I don't know if those kinds of setae are restricted to the legs or can grow on the main parts of the body.
But insect antennae are already used for smell (that's why moths have such complex looking antennae), so olfaction shouldn't be a problem.