Interstellar space is so empty that it's not going to experience significant erosion from micrometeorites even over geological significant lengths of time. The interface points between dissimilar materials can be a source of corrosion, so certain portions of the structure will degrade in the relative short term. I don't know exactly what techniques and materials are used to attach the various parts of the structure, so I could imagine that galvanic corrosion would eventually cause the various booms to collapse and it to turn into a jumble of equipment that is just kind of flying through space. But there's no particular reason that it won't remain a recognizable artificial object billions of years from now - if there's no mechanism for an object to degrade, it just kind of continues existing. Take for example fossils such stromatolites, which are billions of years old, but still recognizable for what they are when examined by intelligent beings.
Will the golden record last a million years? Certainly. A billion? Probably, but there might be some process or environmental factor we don't yet know about that will cause it to degrade. A trillion? That's an awful long time, it seems like a bad bet to make... but it's not out of the realm of possibility.