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

You can wear anything that you have earned in prior service. However, anything you wear will draw attention. Just be ready. I did basic and advanced more than once and I wore my EIB and Jump Wings.

I went through Marine Corps boot camp with an Army Ranger sergeant E 5, who had a tour in VN already. The Marine Corps policy was not to identify those individuals with prior service, so they would not have special treatment (good or bad) either intentionally or otherwise. I believe that non-identity is appropriate for basic....He showed up at graduation with ribbons, badges and sergeant stripes. I think he was proud to do it that way, as well

If you earned them wear them.
Talk to the command.

The comments indicate that the qualifications should be wore. My experience was that we wore no rank or qualifications in Ranger training. We had a Vietnam veteran captain training with us, we all knew who his was and followed his lead. He just stood out from us newbees.

If the Army thought you were good enough to wear those badges at this point, they wouldn't have made you go back to preschool like Billy Madison.

Now think back to your Preschool days? What is the advice for every future service member be it Soldier, Marine or Coastie? KEEP YOUR HEAD DOWN AND DO NOT BRING ATTENTION TO YOURSELF.

Remeber how they found out one kid was a track star? The got smoked by running laps around the formation, some kid was in a band they got to sing cadence in the classroom and suddenly for every movement for a few days...
God forbid Air Assault forgot how to tie a swiss seat, flub a line of the soldier's creed or at your advanced age miss a step on your rucks.... just be the quiet slick sleeved old man and learn the fundamentals like everyone else is there to do.

You can show out with your full stack at graduation and AIT

I would wear them. They know their former service already with you being an E-4. When you graduate, the’ll be looking for them and ask if you’re not wearing them. You may earn additional push-ups for not wearing them.

When I was at Reception Battalion at Fort Sill back in 1996, there was a specialist about to start basic training that was wearing a drill sergeant badge because he had been a Reserve E-5 drill sergeant and when he went active duty, he got demoted because he didn't have enough time in rank to keep it when he went active. The first drill that saw him wearing that lost his mind and asked him why he was wearing it, the guy explained what happened and the drill sergeant said nothing more after that than, "Man, that sucks, Specialist." All the drill sergeants at Reception left him alone after that.

There’s alway that rumor in Basic that CID is embedded in the unit. You might make some of the DSs a little nervous if they are into shady business. Lol

Wear them with pride, you earned them!

The Drill Sergeants already know the background with ya. Like it's been said, wear them and be the positive influence with the newbies. The Drill Sergeants will probably cut ya some slack due to you having to go thru again.