When I was going back through some old late 90s SW Insider mags, someone asked a question about how much control the Empire had at the beginning of ANH. The person answering the questions said that from dialogue in ANH we know that the Emperor still didn't have complete control because someone mentions capturing Leia might garner sympathy from the Senate. So they were still somewhat wary of the Senate. The Emperor also knew starting around AOTC that there were senators who were trying to contain his political power so he knows by ANH they are funding the rebels. So I seriously doubt anyone in the senate would know anything about the Death Star. They were waiting on the Death Star to become operation to dissolve the Senate and take complete control.