No. The radar could observe objects as far as the orbit of Saturn, but typically near-earth asteroids, comets, Soviet ground installations, etc.

It could track celestial positions for about 2.6 hours.

https://en.wikipedia.org/wiki/Arecibo_Telescope#Research_and...

Think about a radar round-trip of 2×12 light-hours; that is 86.57 AU, twice the distance from us to Pluto. Also, the Earth orbits the Sun aside from merely rotating. That radar round-trip would be one cosmic boomerang, looking at nearly nothing.