Can I decline being promoted to Corporal?

I say go to your CSM and Bn Co and tell them about how you feel. I am sure they will take care of you appropriately.

Short answer: You can.
Longer answer: I urge you to not do this. Strongly! This will feel like a slap in the face of people who are saying that they believe in you. Don't look at this as a burden. Look at this as an opportunity to learn, and gain some valuable experience. Yes, your unit might be trying to get some NCO work out of you without having to give you NCO pay. Let that establish your own standards. Eventually, you will be in a position to influence whether a unit expects people to work without the benefit of the pay, and you will be able to tell them all about it, from your own experience. To get there, you will need to have this experience. Learn. Advance. Lead.

There is stupid and then there is stupid on an epic level. Congratulations, you made epic level.

sorry left out the word not, between did and want

I don't see why you cannot turn down the promotion. I turned down a promotion to SGt. because I was getting out in a couple of weeks, and did want to go through all the work for the promotion and getting the strips sworn on (expensive).

This appears to be something new. soldiers do not want to be NCOs. This appears to be a crimp in the system. Why would soldiers be intimidated by authority. Commanders need to address this

yes you can I did I said if I was going to be an NCO your going to pay me. I went from E-4 SPC to SFC in 4 short years. I saw the guy that was my team leader take a corporal position and he was in the same position when I made SFC. I believe that is a war time rank to make you an NCO while waiting on your promotion not someone you can put in charge of mopping the floors and have him scrub the toilets as needed. Be an NCO or not lateral promotions are BS

I know a medically retired Army SSG that made numerous ranks up and down (never below CPL) that has had BDE level positions, without additional pay at any number of those ranks. Yes, they were in combat most of those times.

Rather than quibble and avoid/deflect responsibility, you MIGHT ask your platoon SGT and/or the S-1 clerk if you have been scheduled for BLC. If there's, say 6 months wait, it will help you to step up, if the wait is a couple of years (I've seen it happen, even in the Cold War), refusing the slot can end your chance at a career.

"You pays your money and you takes your choice."

You made the board. From here, what happens is on you. Look at what can happen in 15-16 years...
Retirement? Flipping burgers for low wages? Choose wisely.

When I was in, the Army was top-heavy in NCOs with no slots to move up. I got selected for the board and disqualified on a technicality, when they were disqualifying for even smaller gigs. being in S-1 at the time, my CSM broke it to me and gave me the opportunity to address the board, so, I chewed them out, signed my ETS papers in front of them and instantly had less than 90 days left, given accumulated leave.

Me? I'm permanently disabled, receiving 100% Disability for Individual Unemployability. That means, if I could find work, earn some additional income, anything over 10% of my disability can jeopardize my rating, my income and health benefits. Sucks eating the low fruit, but I've got a Quarter-million Dollar (civilian cost) smile, getting high-dollar therapy for my Service-Connected PTSD, frequent physical therapy for medical issues (result of in-service injuries) and who knows what all else... I've even had genetic testing for hidden syndromes (yes, through the VA).

Ball is in your court. Your entire future relies on what you do NOW. Crap, or get off the pot Specialist.

If I were you I would take the promotion to Cpl and show that you are capable to being a leader which would help you in future promotions.

Yes. Now is a good time to decide what you want in life. Know your worth.