Firstly, it is not the auditors who are responsible for preparation of accounts; that is the responsibility of the management. Auditors (external) only express an opinion on the accounts prepared by the management.
I think there is no requirement for non-accounting staff to be trained in IFRS. But the issue is there may be new requirements for information gathering to comply with IFRS and such information may be prepared by non-accounting staff. In such cases, it is good to educate such staff as to the requirements of the standards so that the information provided by them are free of material misstatements. However I dont personally think such staff need to go into details of IFRS standards but just educating them as to the requirement should suffice.
However for a General Manager, it is always better to have a good understanding about every aspect of the business but there is no requirement for a detailed technical knowledge unless he is from a financial background.