Noup. It won't damage your display I think it should rescale it back to your native resolution. If your display doesn't support 1080p the game won't offer it as an option. Btw be sure to have the right HDMI cable (1.4a) that suporrts 1080p. You can also set everything up from your OS-under display settings.
Edit: I haven't seen ZerroBarrier's answer , but basically what he/she said.
ASUS G75VX
Win 8, i7-3630QM, 2,4 GHz, GeForce GTX 670MX, 8 GB Ram,120 Gb Samsung 840 SSD+750 Gb HDD