Most people likely don't try. You can if you want to. If you plan on having it mailed I suggest using a courier service with good tracking like Fedex or UPS, for example. I do not suggest USPS (which would turn into Canada Post.) However, the cost of the courier service can be expensive so you have to decide if the reason you're going is worth waiting for or not. Generally cards like that are mailed within a few days of being produced.
Because it's been issued and you'll have it when you return, I don't see how it will affect your AOS. It's not like CBSA will want to see the card.