The shampoo looks good (it has a water soluble cone), but the condish has dimethicone (not water soluble). So, yes, the shampoo will remove them since it has coco betaine.
2C/ Coarse/ Normal porosity/ SW Florida/ Transitioning to gray
Cleanse: CJ Daily Fix, JC Cleansing Cream, TJ Tea Tree Condish
Condish: JC Too Shea, CJ Curl Rehab (both as RO & LI)
Stylers: UFD CM, CJ PP, JC Spiralicious, Darcy's Cream Gel & Cocoa bean whip