Can I be excused from Annual Training in the National Guard?

Can you? Sure. Will you? Won't know until you discuss this with your Readiness NCO and Chain of Command. Talk with your professor(s) and ask if you can pass their phone number onto your Commander. If they say yes, give said number(s) to your Commander and request your Commander talk with them to get the info straight from the horses mouth.

Getting excused from AT is no easy task, It can be done, but it takes work and proven extenuating circumstances. You also have to remember that your Commander HAS to meet mission requirements for/at AT with personnel on top of everything else. You could very well be that one Soldier that puts the missions in BLACK status due to your absence. I'm not saying this to discourage you from asking, I'm just saying this to explain to you as to why your Commander may say no. Plus, your Commander will more than likely have to relay your request up to the higher bosses. It's more than just a simple YES or NO when asking. Consider lots of pieces of the puzzle your Commander will have to.

I suggest that you present a plan to perform your AT individually ahead of the unit AT. That plan is more likely to get approved if there is value added to the unit as opposed to vaguely working for the supply SGT. Prepping an area of an inspection, organizing a specific section of supply or admin areas, PMCSing vehicles that are going to AT, performing a specific post AT task such as setting up and washing tents are a few suggestions that come to mind. You could also ask to break this up into week long or shorter sections. If you can be present at the front and back of AT for example you might be able to help with load out and recovery.

"Can I be excused from Annual Training in the National Guard?"

Sure, just tell'em I said it was OK if you didn't show up and if they have any questions to give me a call!