Do good deeds count if a person has no faith?

In the hereafter, no, faith is the foundation that gives deeds their worth. But once a person accepts Islam, even the good he did beforehand is credited to him.

Faith without action and action without faith are both barren. Deeds performed without iman carry no reward in the hereafter. Adi bin Hatam may Allah be pleased with him asked the Prophet ﷺ if his father Hatam Tai who was known for his generosity would get any reward in the hereafter, to which the Prophet ﷺ replied that he was granted what he desired (i.e., Fame). [Musnad Ahmad 120]

However, once a person enters the folds of Islam, his good deeds performed even before accepting it are rewarded. When Hakeem bin Hazam may Allah be pleased with him, a generous man, asked after embracing Islam whether his earlier good deeds would count, the Prophet ﷺ told him: "You have entered the folds of Islam with the good deeds you had performed earlier." [Musnad Ahmad 121] Faith is the basis; once it is there, the good is not lost.