Essentially, there is no religious freedom in Saudi Arabia, and nobody is likely to openly change - indeed:

conversion from Islam to another religion is considered apostasy and punishable by death.

All citizens are considered Muslim by the state (source).

In 2008, the Vatican tried to get a Catholic Church built in Saudi Arabia, and had discussions with the Saudi government, but the result was that it was not permitted.

So that brings us to the Christians (including Catholics) that DO exist in the country. There are considered to be more than a million Roman Catholics in the country, as well as from many others.

From the above link:

Saudi Arabia allows Christians to enter the country as foreign workers for temporary work, but does not allow them to practice their faith openly. Because of that Christians generally only worship in secret within private homes. Items and articles belonging to religions other than Islam are prohibited. These include Bibles, crucifixes, statues, carvings, items with religious symbols, and others.

So, to your question about whether this secret practice is allowed or tolerated? Not so much. They have an entire 'government' organisation - The Saudi Arabian Mutaween (Arabic: مطوعين), or Committee for the Propagation of Virtue and the Prevention of Vice (i.e., the religious police) which prohibits the practice of any religion other than Islam.

The government also doesn't let clergy of other religions into the country for conducting religious services (naturally this means no Christian baptisms, weddings etc by official clergy legally).

And if they find someone practising in their homes? International Christian Concern (ICC) protested what it reported as the 2001 detention of 11 Christians in Saudi Arabia, for practicing their religion in their homes. In June 2004, ICC reported on what it termed a "pogrom-like" crackdown by Saudi police on Christians after media reports of Koran desecration in Guantanamo Bay.