Can ceiling light mount box be used to attach ceiling fan?
Maybe.  

If the box has a bracket that securely attaches it to a framing member, then the box can support a ceiling fan up to 35 lbs.  If the box is not securely attached to a framing member, it cannot support a ceiling fan. According to NEC, ceiling boxes are supposed to be installed so that they can support a 50 lbs fixture (that's a light fixture, not a ceiling fan). However, this is not always the case, especially where the boxes are installed by those unaware of the code requirements, or before it was a requirement.

If the box is designed for supporting a ceiling fan, it will be marked with the amount of weight it can support, up to 70 lbs.  A ceiling fan weighing more than 70 lbs., has to be supported by other means.