Is it acceptable (aka would Apple consider it acceptable) to have a UIPickerView in a UIActionSheet?
Yes. It is acceptable.
set the frame of the UIPickerView
add the UIPickerView to the actionView
As I remember, actionView will be full screen in this case
UIActionSheet *actionView = [[UIActionSheet alloc] initWith...];
UIPickerView *pickerView = [UIPickerView alloc] init...];
pickerView.frame = CGRect(....);
[actionView addSubview:pickerView];
[pickerView release];
[actionView showInView:theView];
[actionView release];