Question

Is it acceptable (aka would Apple consider it acceptable) to have a UIPickerView in a UIActionSheet?

Answer 1

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];