Yes. Just write a sketch that copies all input to the Arduino's serial RX and use NewSoftSerial:: to writes that input to the SpeakJet's RX pin.
Be mindful of baud rate differences or set the Arduino's hardware serial port to match that of the SpeakJet's.
[Edit] Forgot to mention that your Arduino sketch will probably have to buffer input from your PC because the SpeakJet won't be talking as fast as the PC sends. Watch the SpeakJet's Half-Full pin.