Can I decline being promoted to Corporal?

Really? I suggest you seriously take some time and fully reconsider if a military career is really for you. Rank or no-rank, higher pay or not, a real leader steps up, especially in difficult times. If your fellow soldiers learned about this do you think they would want to follow you?

God bless any Man that knows his own strengths.
You know your "techs". You know your fellow BN-mates. You don't want to make life-deciding decisions.
To me, Brother, you're more of a Leader than many that outrank you.
Got room in that foxhole?

Yes, but you would be hurting yourself by not taking on the responsibility your command believes you can handle. Don't think about the money think about your place in the Army and the men under you that you can shape in being the best at what you do and the SGT promotion will follow in do time. This will prove you deserve your promotion.

This is what’s wrong with the military now. Most service members join and see the military as a job, not a profession of arms. People think they should be picking and choosing things that they want to do or appeal to them.

Why would you? I guarantee you that your Bn CSM has a long memory. Take it. The recommendation shows that the Bn's senior NCO has confidence in your leadership capabilities. Why would you throw that away?

You're freakin kidding right?! You need to quit being a chavala and accept the rank given to you.
The pay...stfu respectfully. So what Army pay is dookie anyways you still doing the grunt work.
Just you'll do it with rank on your collar. Waaaaa my mommy waaaaa....
You're seriously sounding like a blue Falcon now think of all the troops you can help or square way.

but if you're an s bag then that's probably why you gotta problem with the rank. also you like the shamptastic world I get it.
Think about it if any of your so called buddies does some s***** s*** knowing that you have that rank and putting you in a position then they're not your battle. SMOKE EM....

In closing take the rank or whatever school you need to go to come back get the 3rd stripe and STFU Roger that carry on.

Ps I woulda killed for 2 Strips feel honored. Hooah

I'm going to bounce around with my response, but it's based off what I see visually and my own experiences. Looking at your profile, I'm a little confused...your title lists "SGT", but in your posting I believe you're a E-4(p). It's always best to have your profile match your actual status.
To answer your question, as many have, you can definitely decline the promotion, but there are a few things that stand out...your command believes your capable of doing the job (which you should be proud of), but feel that some type of schooling should be completed first, which is not uncommon. If you were my troop...you've now burned every bridge I've ever given you or planned to give you! Corporal is an "NCO", a rank that should be worn proudly! As an "NCO", what are your priorities? Accomplishing the mission and taking care of your troops! That means your troops eat first, get paid first, get to leave for home first and are highly trained most likely with assistance from YOU or directly by YOU, so they actually come home...you are the one that saves their ass! Any "leader" that demands more pay before doing a job...is not a leader, they're a lazy ass leach.
If you read this to the end...wear whatever stripes you get proudly, without request for additional pay or recognition. As your performance is recognized, you'll get the praise, you'll get the schools and the recommendations for promotion. Lastly, if you can't put your troops ahead of yourself and if you're going to ask for money before doing a job...then I recommend leaving for the civilian sector.

OMG, ALL RANGER team members are team leaders in their own right. Right now your mind set is not ready for leadership or RANGER School. Go wipe your nose and come back when the back bone has become a little stronger.

As a CPL, I can say you can decline. It is not recommended if you intend to become a SGT, but if your intention is to try for Warrent Officer; talk with your chain of command - most NCOs will understand the urge to become a specialized Officer but you are going to have to do the research. Otherwise, take the CPL for it's leadership potential and be ready for tasks above your rank. I filled a SFC position, based on my experience and knowledge. The respect from your soldiers will be there but you will still have resistance from the higher ranked personnel. Think it through and do some research...

I was the platoon mechanic as an E4... many high skilled (not) folks above me who could've done my job (again, not even close).

I had an E5 who wasn't allowed to carry his rifle, E7 who was sent home early negates his wife got pregnant and he lost it. Many other 5 n 6 who couldn't step up and even begin to read the manuals to any MRAP or brain m think to begin on how to maintain it. Not did I learn and review m recite, I did the job of my mechanics to ease up on them.

Yes you can deny and you'll still be given leadership roles.