The abillity to play 1080P or not is not a situation of being limited by the drive or not. The Blu-Ray drive simply reads the data off the disc.
The limitation would be whether your rig would be able to decode it at 1080P or not. I've never seen any performance numbers of an E6700 with no hardware assist video. You would see very smooth playback with just an 8400GS or a HD2400 though.