NoNot if you want to communicate with it
Undetectability is impossible if it needs to send you something. In fact, the moment it needs to send a single beep from orbit with non directed antennae, that beep can be picked up by at least one NATO country, because radio waves go out in a sphere and it is flying so high, that every point over the Soviet Union is at least observable by some NATO or commonwealth country in the first or second reflection.
If the satellite flies the Sputnik 1 orbit, then it will be at its closest about 215 kilometers over earth. The ping will be listenable for 1670 kilometers - or when it does it in the center of Russia, it'd be listenable to most of Kazachstan and some areas of Mongolia and China. The first and second reflections carry the signal to India and Turkey. At its furthest, 939 kilometers over the earth, the ping reaches 3586.1 kilometers in the first instance and that means at the same point the unreflected signal can (almost/barely) be picked up in Deli, Oslo, and Ankara, and its first reflection will reach Tokyo and Berlin.
In fact, just about 230 kilometers more west and it can be heard in Berlin and only 1200 kilometers to the east to reach Tokyo instead of Ankara. And in any case, Spitzbergen is a very good listening post, allowing to hear the signal when it has about 3000 kilometers ping radius - which is at a height of 670.3 kilometers over the marked spot.
To visualize: these are the minimum and maximum circles of the direct signal, and that is without taking into account the effects the upper atmosphere has on signals - which usually make it carry much further.