Umm, no. It's a booster of an orbital rocket, the booster itself is not orbital. Falcon 9 stages super early even compared to other rockets, specifically so the booster can come back before it gains anywhere near a significant fraction of orbital energy.

This is great because it does make it practical to recover the booster, but it's only possible by making the second stage significantly larger and more powerful than comparable rockets that stage later.

If the booster got up to orbital velocity, it would burn up just like the Rocket Lab "mothership" host satellite that accompanied the Varda capsule. They were coupled together, the mothership performed the braking burn to adjust their orbit into a reentry trajectory before the two separated. Only a minuscule amount of drift separated the two as they hit the atmosphere, but while the mothership burned up, the capsule survived.

If Falcon's booster achieved orbit, it would burn up just the same. The only reason it doesn't, is that it's only going a tiny fraction of orbital velocity when it comes home.