The existing fixture mount needs to be able to bear the weight of the ceiling fan.

How can I tell if it will?

One easy way is to hook a sling to the mount and load the sling with weights to simulate the load of a ceiling fan. If the mount is deficient, you may get a bigger hole in the ceiling.

Even if it passes the load test, you should still get the mount looked at.

If you're thinking of having lights with the fan, you will need to run an additional circuit.

In which case, you probably would end up installing a new mount anyway.

Here is a link that might be useful: Installing a ceiling mount bracket electric box