I'm in the "doable, but why?" category. Why do you want to commit yourselves to what, in essence, would be a high stress death march.
I've met folks trying to do what you are proposing, and they were miserable. Their feet were a bloody wreck (and I mean that literally) they never really MET anyone on the trail, they were constantly pushing, never had time to stop and smell the flowers, or the pines, or the ramps, or whatever.
Why do you want to hike the AT? Are you just putting a notch in your belt? If so, cease and desist. The AT isn't an extreme sport. Nor is it some elite training ground. At it's simplest, it is a long vacation. At it's most profound, it is a sacred journey of the spirit.
If all you want to do is punch out the miles and say you did it, then cut out the middle man, go down to Mexico for the Summer, come back and say you hiked the AT. No one is going to call you a liar, because no-one will know one way or the other. Sure you will be cheating yourself, but if you run through the whole 2170 mile trip, you'll be cheating yourself anyhow.
Someone once suggested that there should be an award for the longest continuous thru-hike (without excessive town time). I tend to concur with that. I'm not just saying that because my hike was long (6 months, 8 days), but because in that 6 months, 8 days, I still felt like I had to rush and was missing stuff I ought to have spent time to see. There are a thousand blue-blazed side trails to waterfalls and scenic overlooks, little loop trails leading into little coves and grottos. They shouldn't be missed. You could spend a month hiking the various loops and side trails in the White Mountains alone, and The Great Smoky Mountain Park deserves far more attention than most thru-hikers give her. The same for the Shenandoah, and Grayson Highlands and Mt. Rogers State Parks.
If you really want to hike the AT, don't rush it. Don't squash it in between two other goals. Give it its due. Wait until you graduate and do it then, when you can give it the time it needs to be truly savored. If it is so important to you that you cannot wait till you graduate, then take a semester off and give it a solid go.
I got the bug to thru-hike the AT when I was a 21 year old soldier sitting in a hospital bed at Ft. Benning, GA after breaking my leg in a parachute landing (the jump went fine, the landing sucked). I saw "Five Millions Steps" on the television and knew exactly what I was going to do when I got out of the Army. When it came time to outprocess I had no money, the economy sucked and I had few prospects for making money. I put off my hike, married my sweetheart, went through a series of crummy temp jobs, divorced my sweetheart, and then inherited some money from my grandparents. I took that money and whatever I could save up, and hit the trail. I was 26 years old and turned 27 on the trail just South of Rangley, Maine.
I spent a ton of time on the trail and spent my credit card into the ground to support my hike and get the most I could get out of it without worry. That was a great 6 months and I learned a lot about myself on that hike, not all of it pleasant, but it was good to know. If I had been rushing to meet my original goal of a 4.5-5 month hike, I wouldn't have met a lot of great people or seen a lot of great things. Sure it took a couple years to pay my way out of it, but that was OK. I only wish I had another month of it.
Give it the time it deserves, or don't bother at all.