You are not able to do either, unless you are prepared to take the risk of being caught and getting a criminal record.
Benefits are not available when you have elected to go on a training course under any circumstances.
Student status is probably more flexible, however since the Treasury has deliberately classified flying training as a leisure pursuit rather than a training course, it is unlikely you will obtain student status. Unless your course is proactive enough to approach the NUS and sort it out (by paying a fee for accreditation)...