I agree with Mindblade's response. The luck doesn't seem to have any bearrance on finding rare animals. The luck helps for critical hits and spells that have a status disorder, Gibarta. When I first encountered an Al Rappy the result was very similar. I received Flowen's Shield. The second time I received ... Freeze Barrier
Yes, your section ID does matter as to which mag you'll get from the cell. You can either receive a Soniti or a Pirtori from mag cell # 502. I don't know about ID's not having a mag cell available.
One side not is that a friend received a mag cell from a Booma. Now that we know it doesn't have to be Al Rappy's it broadens the field. No longer will I be playing through Forest 5 times a day looking for a cell. Hope you find one