Based simply on the peak temperature a PCB experiences during selective soldering, I can confidently say that you will not have any problems soldering an LCD glass display into your assembly.
Whereas your hand solder iron is at 700F as you say, most selective soldering (at least on our machines) occurs at a tip temperature of 280 Deg C or less. This has obvious advantages not just to the LCD display;in additionyou will notice an absence of measling, lifted pads, etc. on the PCB itselfwhen using a properly configured selective machine.
Speaking for our company only, we have done several samples for customers that had your exact application of an LCD glass display, in addition to customers using our machines that run that application every day.
It isn't clear whether the LCD is on the solder side or the secondary side from your question, however, ACE has successfully processed boards of both configurations.
I would highly recommend a selective process to anyone looking to improve their through-hole process control and quality, especially if there are heat-sensitive components and PCBs (such as Teflon) that are otherwise vulnerable to a rogue soldering iron.