Can I wear my Airborne and Air-Assault badges while in basic training?

Move in secret until your intentions need to be revealed. Wear them at the end, so others will look at you and go "oh wow". Wearing them early will just bring unneeded attention in basic. I'm assuming you have no lessons needed to be learned in basic, so I would fly under the radar until close to graduation. This is not a time to brag, just my two cents.

Wear them! Airborne all the way!

Everyone is telling you to wear them... This should have been something you could answer for yourself. But it depends on who you intend to be by re-entry into active duty! I will be the devil's advocate here and present you with the alternative that no one has yet said..... Nah man, if be a total pussy and not wear them. Don't attract attention and totally stay in that Spec4 mentality! Look to sham responsibility rather than shoulder it up and step up like a future leader of men and women!

The funny thing is they are going to know ..... They will be briefed on the fact that a Spec 4 is going through basic. Other than as a College Graduate it would be the only reason for such!

As a Drill Sargeant for 4 years in BCT and as a 1SG in a BCT unit I would suggest you wear them proudly. On the flipside as a Drill Sargeant and a BCT 1SG and found out you were not showing your pride because you were not wanting to be a leader and not wearing your credentials of expertise duly earned you would think someone started up a weedeater and dropped it in your drawers. Believe me that is something you are not going to be successful at hiding anyway. If you are desirous of being a soldier BE ALL YOU CAN BE.

I met a Soldier once wearing an EIB even though he was entitled to wear a CIB. He said he earned the EIB. He was kind of smart-alecy, but it points out that the pride of personal achievement comes from within and not from what other people think.

When I was in Army basic in 1984, we had a soldier that had been in Vietnam. He waited until graduation day when we were all in our greens to show all of his awards. He was more decorated than any of our drill sergeants. I would recommend you wait until your graduation. You will gain the respect of the other trainees and your drill sergeants.

I was also in after a couple of months after my discharge the job market was so bad I reenlisted. I was sworn in a MEPS in my class A uniform. Made a big impact on the new recruits.

ask your unit

When I enlisted in the Army in '71, with PS as a Navy/Marine Vet, Vietnam was still going on. Myself and another PS (Army 1st Inf Div) were both Nam Vets. Literally, the Drill Sgt's decided they didn't want "old salts" in BCT. I assume that was because DS' were short staffed and they often used recent graduates as "Acting SGT's" while they were awaiting orders, or AIT start dates.
The actually sent us home with instructions to call our DS every Sunday. I think I was there four times after the day we got assigned to a BCT Company. That was for things like "Night Fire & morning rifle qualification, PT Test and Puggle Stick, Hand Grenade throw and Graduation.
At Graduation, the Co Cdr order the two of us, AND his XO to sit in the stands because we all had combat ribbons/badges while he only had the Nat'l Defense ribbon. The XO was a 1LT with multiple Silver Stars, Purple Hearts, etc with about 5 full rows. He was a Mustang and was part of the Army's RIF, despite his years of experience.
Anyhow, you should consult with your Drill Sergeant before just showing up in formation with all your AB and AA badges. Being an E4 will already subject you to scrutiny and likely land you in the senior Recruit Leadership position if you're the only PS in the Company. Some DS will not like the idea of you wearing badges; others may PREFER that you do and will likely point you out as a positive example to the FNG's.

This is an opinion only. If Regulation allows you to wear them, wear them, you earned them, you are qualified for them, be a leader among your peers, set the example of what a soldier should look and act like. Your not replacing a Drill Sergeant by any means, but you can still conduct yourself to the professional standard in which you were trained. However if you are wanting to have them to act all jacked up and shove superiority over your peers then you might just wanna think your motivation to start with. I promise you if regs allow you to wear them you will certainly stand out, but again take the recognition to encourage others to be the best they can be.

You can were anything you want, just have the paper to prove it. However, There's a Thai saying, "The dog barks don't bite, and the dog bites don't bark." Like LTC. Slaton said is correct. Also, one of Murphy's laws, "On the battlefield, don't be conspicuous, the enemy may not see you."