Sort answer is “no”.
Long answer is to use sunrsasign Provider, which implements RSAKeyPairGenerator such that the public exponent is 65537:
*”/**
* RSA keypair generation. Standard algorithm, minimum key length 512 bit.
* We generate two random primes until we find two where phi is relative
* prime to the public exponent. Default exponent is 65537. It has only bit 0
* and bit 4 set, which makes it particularly efficient.
**/*
if you want a different public exponent you need to create your own provider and integrate it with JCA.
more on the math behind this here.
solved Java RSA private key generation when public key is known