I do not see that this would happen: the Senate was made irrelevant the day the Second Triumvirate was formalized, and the closest it got to reclaiming power - 41 AD, via the assassination of Caligula - showed that it was no longer the Senate but the army that called the shots. By any date by which the Byzantine Empire is formed (284, 629, you name it) the Senate was already irrelevant. Moreover, during Imperial times the status of the Senate depended on the good will of the Emperors. In other words, senators were the Emperor's admirers, friends, courtiers, and advisors - their power depended on him, not the other way around. The nature of Imperial autocracy - i.e. the doctrine of One God, One Empire "on Earth as in Heaven" - made this virtually impossible as well.
Despite all the coups, revolts, etc. that happened in Byzantine times, it is telling not one was concerned with changing the nature of the throne -- only which faction would occupy it. The power brokers in the Empire were the always from the army and the bureaucracy ultimately, not the Senate.