What you mean by a certificate is also of importance
do you want staff to have the Level 2 Award in Food Safety regulated qualification or just a certificate to say they have attended the training?
Regulated qualifications can only be booked and administered by a registered training centre,
There are plenty of accredited courses you can obtain but most do not allow you get the qualification - so be clear about the outcome you want
From an auditing point of view exactly as pHruit has said with internal training of this nature I would want detail on the content of the training and the capability of the trainer
It is certainly workable and I know a few companies who are registered as a training centre with their own 'trained' trainer.