Just match the serial speed on the serial monitor display (bottom right hand corner pull down) to the serial speed of the GSM (in your case 19200). I don't have any problems using serial port monitor to display data at the same time the hardware serial port is connected to the GSM. Basically all I am doing, for now, is I issue an AT command to poll the GSM every couple of seconds or so to see if there are any unread messages (the return info is stored in a buffer) and I dump the buffer onto the screen to make sure it collected data and then I grab the GPRMC using NSS and dump that buffer onto the screen to make sure I'm receiving that data correctly. If you want to print text out to the screen my advice is to try and be careful of your choice of words because you could inadvertently issue more AT commands to the GSM module. Case in point I try not to print the word "DATA" because of the AT in the middle of the word. I've seen some people automatically issue a simple "AT" after printing anything to SPM to, in essence, "reset" the communication to the GSM. I've also used Serial.begin() after printing which seems to work well also.
Wayne