Hi!
As far as I know you will be invited to write the FEAST test, if you have sent your CV and all the other necessary documents (copy of the language exam result, and your school leaving exam (érettségi)).
Also when you will sign the contract, there is a point in it, which says that you cannot leave HungaroControl at least for 5 years if I am right, otherwise you have to pay back your training cost. So yes, this means, that if you finish with the training, you will have a job.
Tamas