Yes, but they didn’t know about the Rule of Two
At least one Imperial thought along these lines: soon-to-be Grand Moff Tarkin. He went even further and concluded that the missing Sith was Emperor Palpatine:
The matter of precisely how the Jedi had been killed or the Emperor’s
face deformed had never been settled to everyone’s satisfaction, and
so Tarkin had his private thoughts about the Emperor, as well. That he
and Vader were kindred spirits suggested that both of them might be
Sith. Tarkin often wondered if that wasn’t the actual reason Palpatine
had been targeted for arrest or assassination by the Jedi.
Sidious assumed that if Tarkin knew that Vader was a Sith, he would have suspected that Sidious was his master.
Sidious assumed that Tarkin had puzzled out that Vader had once been
Anakin Skywalker, under whom Tarkin had served during the war. Tarkin
may also have determined that Vader was a Sith. If so, it followed
that he accepted that Sidious was Vader’s dark side Master.
Why did other Imperials not suspect something similar?
The truth is that knowledge of the Sith was not widely available. The Jedi often seemed reluctant to reveal even the very identity of their foe to the common people, let alone details like the Rule of Two. Further, there was a systematic effort by the Empire to eliminate all details of the Jedi and the Force from public knowledge after Order 66 was executed.
“We no longer speak of the Jedi,” Mas Amedda had said when they had watched Vader issue his warnings to members of Coruscant’s underworld.
It struck Tarkin now that the Chagrian’s attitude wasn’t one that was
confined to the Emperor’s court. In the five short years since the
Order had been eradicated—Jedi Masters, Jedi Knights, and Jedi
Padawans wiped out by the very clone troopers they had commanded and
fought beside—the Jedi already seemed a distant memory.
As such, it seems unlikely that he would have allowed information about the Sith to travel far and wide. Even Tarkin appears to have concluded that Sidious was Vader’s Sith master, not because of the Rule of Two, but because he reasoned that Palpatine was Sith and obviously Vader’s master.
Not many people even knew what a Sith was. Of those, how many would have associated red lightsabers with the Sith? Of those, probably none knew of the Rule of Two. Did the Jedi even reveal it to anyone else?
- Few Imperials knew about the Sith before the war, and probably mostly the high-ranking ones.
- Fewer Imperials knew that Vader was a Sith.
- Basically no one knew about the Rule of Two.
- Few people were as close to Palpatine as Tarkin, nor as intelligent, which would be needed to note the similarities in outlook between Palpatine and Vader.