Did Itachi kill innocent people when in Akatsuki?
Canonically, there is little to no information regarding Itachi's missions while in the Akatsuki. So we cannot say for certain whether or not Itachi killed people during his missions; innocent or not.
If you consider some events that are shown within the anime, then yes - Itachi more than likely committed murder (innocent and non-innocent alike) while in the Akatsuki.
Let's look at some examples:
(Non-Cannon) While Itachi was in the ANBU, one of his specialties was assassination:
From his time in Anbu, Itachi became proficient in stealth, infiltration, and assassination.
Because of these skills, the Akatsuki utilized him (along with Jūzō) for these types of missions
Jūzō and Itachi worked very well with each other, being involved in at least three missions together, which involved assassination and sabotage.
(emphasis my own)
(Cannon) During the "Search for Tsunade" arc where Itachi is first introduced, he tortured Kakashi with Tsukuyomi, showing no hesitation. Following these events, Itachi orders Kisame to kill Asuma and Kurenai
Itachi instructs Kisame to capture Kakashi to find out what else he knows and kill the others..
If Kisame were to succeed, while not dying by the hand of Itachi, he gave the order to do so.
Having Itachi killing innocent people to comply with his infiltration would put his character and the third Hokage who agreed with this, in a very different shade / position, possibly even putting in risk of potential war scale conflicts with other countries to the land of fire.
In the public eyes, Itachi was viewed as a villain who defected from Konoha. Despite the reason behind the Uchiha's massacre, the true purpose was hidden to only a select few. If other countries within the Land of Fire were to declare war, it would be against the Akatsuki, not necessarily against Konoha.
Itachi had to do what he needed to do to maintain his covert mission. If he were to show any sign of remorse or hesitation on missions, the Akatsuki would have questioned his purpose for being there.
