Yes. You'll probably run into problems related to Arduino Due's hardware serial code.
The worst problem is Due's flush() function returns too soon. Here's their code:
Code:
void USARTClass::flush( void )
{
// Wait for transmission to complete
while ((_pUsart->US_CSR & US_CSR_TXRDY) != US_CSR_TXRDY)
;
}
The trouble is the TXRDY flag indicates when the UART is ready to accept the next character of data to transmit, which happens before the final stop bit of the currently transmitting character has been sent. If you rely upon this to clear the DE pin, you'll turn off the RS485 transmitter too soon.
Arduino Uno had this same bug for quite some time. It was finally fixed when Michele Mazzucchi
ported my code from Teensy to fix Arduino's Serial.flush().
The other problem you're likely to encounter is Due's lack of transmit buffering. Due's write (and therefore print) function does not implement a buffer. When you use Serial.print(anything) or Serial.write(buf, len), only the first 2 bytes go into the UART quickly. If you write more than 2 characters, the function just waits until the UART's 2-byte buffer can accept the last 2 characters.
Arduino Uno has implemented transmit buffering since Arduino 1.0. Teensy has had it much longer, since Arduino 0016. Even using just one serial port, this really makes your program much faster, since you can start doing other work while a block of data from Serial.write() or a string from Serial.print() is transmitted from the buffer.
If you're using more than one port, the transmit buffering feature is pretty much essential to maintaining simultaneous data output. Arduino Due gives you 4 serial ports, and they work great if you're mostly receiving data and you only need to occasionally transmit, or you mostly transmit on just 1 port, or if you transmit only 1 or 2 byte messages with delays between them.
Arduino Due is an amazing piece of hardware, but if you're building an application that sends any substantial amount of data simultaneously on multiple serial ports, you'll quickly run into the limitations of Due's software.