...do you think that the email itself is sufficient to document that they were trained.
If your bank's only BSA/AML training consisted of sending an e-mail your examiners should cite you for a "pillar" violation when they walk through the door.
Beyond that, my nephew was having trouble in school and his teacher suggested that he get his eyes examined. The ophthalmologist said he was pretty much blind as a bat, suffering from the same impairment that I have.
His Mom was very embarrassed and as soon as they got outside confronted him: "Why didn't you tell me you couldn't see!" With the wisdom of an 11 year old he responded, "I thought I could!"
Asking people to sign a paper saying they understood their training is more than a tad ridiculous. How would they know if they misunderstood it completely?
If you do not test your employees your examiners are simply obliged to do it themselves. Your methods will be kinder. Training without testing is like deer hunting in the dark - you will not know whether you hit it or not.