You certainly may if you wish to aerate and feel that it needs it (or you see the symptoms of poor aeration).

Two years in, mine definitely doesn't need it. I'll be doing it at least once more anyway.

My first organic mentor on GardenWeb aerates and composts every fall. Aeration has nothing to do with your choice of soil amendments, it has to do with air in the soil.

Back in about '02 I got into this discussion with a lawn care provider in Phoenix. At that time I was convinced that organic lawns didn't not need aeration and that chemical lawns did. After considerable heat and some light, I learned a lot from that guy. I have come to understand that water control is the key to aeration. Assuming you don't have soggy soil with an 18-wheeler driving the air out of it daily, you can manage your soil air by keeping the soil moist enough to promote proper fungal growth. It is the fungi in the soil that keep the soil fluffed up and open to air (and water). If your soil is hard when dry and soft when wet, that's what you're looking for.

Water deeply and infrequently. I water for 1-3 hours, depending, and I do that only once a week unless it rains.