Yes. The product description specifically mentions washing hair after styling products as one of its intended uses. Its job is to remove excess oil and impurities from the scalp and hair, which includes the residue left by gels, waxes, sprays, and similar styling aids.
Because the cleansing base is milder than intensive shampoos, it can handle everyday styling residue without leaving the scalp feeling tight. If you use a small amount of styling product, one normal wash is usually enough. If you use heavy or water-resistant styling products, you may need to shampoo twice or rinse the hair thoroughly before applying the shampoo. That is common practice with any mild shampoo and does not mean the product is not working.
For best results, focus the shampoo on the scalp and roots, where oil and product buildup tend to collect, and let the suds run down the lengths as you rinse. This helps clean the hair without over-washing the more fragile ends. If your hair is long or porous, follow with a light conditioner on the lengths to keep them manageable.
If your scalp is very reactive, patch-test first and stop use if any irritation appears.