I think answer is yes.
CBI can register an FIR when
1) It receives information
2) After receiving information, if it holds an preliminary inquiry,
3) Then after inquiry only, if it thinks fit, it can register FIR, and thereafter it can investigate.
4) CBI can investigate a crime falling in some State, only and only if State Govt refers to it or if Supreme Court or High Court so directs.
CBI is under Delhi Police Act but after FIR is registered it has to investigate and proceed as per Criminal Procedure Code.