I'd guess it would just continue counting as it should. In the example below I used a fake millis() counter, same variable type, starting at 20 secs before overrun (2^32).
unsigned long virtualmillis;
unsigned long LCDtime = 0;
void setup()
{
Serial.begin(9600);
}
void loop (){
// fake counter, to not have
// to wait 50 days
virtualmillis = millis() + 4294947296;
if (virtualmillis - LCDtime > 3000) {
//Has it been 3 seconds yet?
LCDtime = virtualmillis; //update the timer
//UpdateLCD(); // Change the LCD messege
Serial.print ("LCDtime : ");
Serial.print(LCDtime);
Serial.print (", virtualmillis : ");
Serial.println(virtualmillis);
}
}