No, clean clothes won't be more expensive. Although sourcing companies may well say that they will be, as a tactic to avoid implementing the labour standards that are included in the CCC code.

Actually, this claim is ridiculous. Total wages are never more than 5% of the total cost of an article of clothing. That means in an extreme scenario, if wages were to double and the cost of this were passed along to consumers, a pair of jeans that now costs 41 euros would then cost 43 euros. And there's certainly an argument that these costs should be borne not by consumers but by e.g. the brand name or retailer who take the lion's share of the profit (at 33% and 50% respectively in the case of a US$100 sports shoe made in Indonesia).

At some point there may have to be improvements beyond increasing wage levels to the living wage standard, such as better lighting, ventilation, meeting safety regulations, etc. but this still should not mean that 'clean clothes' will be expensive.