That may well be the case. But it's difficult to say.
On the one hand, he did order the execution of his own son (and watched it!), and he does threaten to kill Thrakhath at at least two points (one at the end of SO2, and the other... hmm, somewhere in SO1?), so clearly, he could be pretty ruthless. On the other hand, who can tell? Maybe as time went on, he became increasingly attached to Thrakhath.
It is also possible that after all those setbacks, the Emperor just wouldn't be able to execute Thrakhath and stay in power. Executing Thrakhath would mean taking personal responsibility for all the defeats - based on what we read about the interactions between the Emperor and the clans (and particularly Baron Jukaga), this could have been the final straw leading to an overthrow. We'd already seen Khasra attempt to kill Thrakhath. In that situation, the Emperor probably would have remained alive... but would he retain any power? And that was in the family, Khasra was Thrakhath's cousin - what would happen if the other clans simply refused to accept another heir from the Kiranka clan?