Yes you can, there is an Application/Software that can restore the DVD to a USB stick, you then can startup from the USB stick by holding the Option key at startup.
But, sadly I can't remember the name of the software, give me a bit, I will do a search, I'll report back if I find it.
Got it, it is called TransMac, they have a 15 day trail.
You don't need any external software at all. I just did the same on my 2009 MBP, which also has a broken optical drive. Do the following:
1) back everything up
2) format a flash drive partition (>7GB) as Mac OS extended (journaled)
3) use Disk Utility on another Mac that has a working optical drive to create a disk image of the DVD onto the partition of the flash drive
4) reboot your MBP holding down the option key. Then select the correct partition of the flash drive as boot up disk, and follow the instructions. It worked like a charm for me.