what does a bluetooth module do if the computer (receiver ) side doesn't pull?

I let my arduino send through bluetooth module (SparkFun Smirf) to computer (Mac running a python code using python "serial" module):

ser = serial.Serial('/dev/cu.Bluetooth-Incoming-Port', 115200) #
while (True):

what if I just remove the read() line and let the python code simply keep an open serial port open?

if the Arduino side and Smirf module keeps sending, what would happen? bytes are simply dropped? or Smirf would stop? I'm asking this because I am getting some random connection drops on the Smirf, not sure if this is the reason