Yes! In fact the full Ak Su Traverse trek includes almost the entire Ala Kol route, except for the hike down through the Karakol valley.
The Ala Kol trek is a 3 / 4 days trek, starting and ending in Karakol. It is interesting for people who just want a few days of hiking and not do the longer Ak Suu Traverse trek.
A typical 4 day Ala Kol route look like this :
Day 1 hike up from Karakol gorge to the Alpine camp (14 km), day 2 Alpine Camp to Ala-Kol Lake (12 km), day 3 Ala Kol Lake to Altyn Arashan (15km), and day 4 from Altyn Arashan to Ak-Suu village (14 km).
Or in 3 days, you can hike up from Ak-Suu village to Altyn Arashan, day 2 hike to the pass to see Ala Kol Lake and return to Altyn Arashan ( 20km) and 3 day hike back to Ak-Suu (14 km)
There are various hikes that do part of the full Ak Su Traverse, there are 3 , 4 , 5 and 6 day variations, starting and ending in different places.