I'd imagine that if it could accept a 1080i signal it would just display it as 1080interlaced lines. IE Not progressive...This would be the sensible thing to do. It should be able to draw the 540 lines of each field but you won't get the full horizontal resolution due to the limitations of the projector.
The CINE 6 is compatible with 1080i as it capable of running sources with a horizontal range of 32kHz. As the retrcae time of the CINE 6 is very close to the blanking time of 1080i, you might loose a little bit of information on the right and/or left side. This is however normal and is also done in most RPTV or Television sets.