As long as the television supports 1080i mode (I haven't seen a tv that can do 1080p that doesn't) then yes it will work fine because 1080i is lower quality.
The I and P after it simply means interlaces and progressive, the diffrence is interlaced does every other line the first frame then switches for the second frame, going back and forth so fast you don't ever notice it. progressive on the other hand displays every line every time. thus it's better quality.
