Low level explanation of how a message is sent via RSA
How it is done in practice is that no one uses RSA to encrypt messages. They use RSA to encrypt (and sign) an encryption key, and then encrypt the message with the encryption key. They send the encrypted key and the encrypted message to the other party. The other party uses their RSA private key to decrypt the key, then uses that key to decrypt the message. Furthermore, in practice, they also add padding to the key before encrypting it with RSA.

That said, RSA can indeed encrypt any message that is smaller than the modulus N. So, if your byte stream in the question is smaller than the modulus, you can encrypt it with RSA. If the byte stream were larger than N, you could theoretically break it up into smaller messages and encrypt them individually. The problem with this is RSA is deterministic; so you'd have to add some random padding to make it non-deterministic. Typically people just don't bother with RSA for bulk encryption, however.