I use Asajj as the leader of my Nightsister team for a couple of days. Her leader ability it on 5, so she should give all NS 24 speed.
I expected to be able to attack at least with Old Daka (speed 120+24) and Nightsister Initiate (112+24) most of the times before Darth Sidious has his turn. Since I don't know his actual speed, I can only assume that a not fully maxed Sid (I am lvl 56 and the opponents were lvl 50 to 55 the last days) has a speed of 120 to 130.
Most of the games Old Daka were first of second to attack, but Sid was never later then second. So it seems like the leader ability isn't working at all or at least not working properly first round. When I played in other modes, I obviously don't know what stats the opponents have. But it seemed like the ability is working sometimes, when all the NS are attacking before other characters that don't get the buff. But in arena the speed seems just not different to what I expect without any leader speed buff.