I also think if you have ICAO English Language Proficiency Level 4 you are good to go.
No you are not!
A Level 4 is a base level of English that ICAO have deemed suitable for the operation of a radio in an air traffic control environment.
It is not an indication of anyone's ability to attend and successfully pass a course run in the English language and neither is ICAO Level 5 or 6 for that matter.
The ICAO ratings are for speaking and listening only.
An IELTS certificate or equivalent is what is required.