Arecibo was until it sadly collapsed last year, not just a large radio telescope but the largest radar disk in the world. Larger radio telescopes lacked that feature. In space you could exceed it without the obvious scaling issues of such a large structure and its weight.
You also have heat as a problem. That space is cold is a bit or a misnomer. The problem with space is that its a near perfect vacuum so things tend to stay the same temp unless they are in direct sunlight. And if they are its hard to dump that heat.
With appropriate thermal imaging it would be pretty easy to tell a spacecraft apart from rocks because it will be making its own heat. Since radiation is the only reliable form of losing that heat you need large radiators on your craft like the ISS has. But those run contrary to good stealth design practices.
There is also the matter of orbits and how natural objects simply aren't going to have certain ones so no matter how innocuous you may look, if you are taking a path only a spacecraft would take nobody is going to be fooled.