No, not really.
If you change the IV to a secret value, you prevent the attacker from checking that the key is correct by comparing to the IV, but they can still check by actually using the key. And if you make it a secret value, you need to pass it to the decryptor somehow, so it can be checked by the legitimate user.
If you choose another constant, Kerckhoffs' principle would suggest assuming the attacker knows it. E.g. if you used it in some server software and the attacker got access to your server they would see it.
There is no convincing security advantage to changing it at all. Its precise value does not affect the security of the key-wrap algorithm. The only reasons you would change it are those mentioned by NIST (pdf, 220.127.116.11), like to accommodate key-lengths that are not multiples of 64 bits (e.g. unpadded 3DES keys).