No, they are fully funded by adverts and licencing their programmes to other channels and platforms. See the 4th question in this FAQ:

https://www.channel4.com/corporate/about-4/operating-respons...

There's been a fair bit of misunderstanding around Channel 4 since Nadine Dorris (ex Secretary of State for Digital, Culture, Media and Sport) aanounced plans to sell off Channel 4. A lot of people never reaslised it was publicly owned and then assumed it was the same model as the BBC, but with some adverts.