Yes you can! If you are watching on a front projection system with a 96x54 screen. I see scan lines with 1080i, none with 1080p and 720. It can be very distracting! I will always take 1080p over 1080i! If I did a double blind test you could tell the difference every time on my size screen.
On something this large you need to use progressive every chance you can.
You would definitely see a big difference with live video material.
Film material, you shouldn't see any difference at all. If you do, you should look into improving your system's deinterlacing capability. 1080i film material at 24fps can be perfectly converted back to 1080p. There is no temporal difference between the interlaced frames, so it's simply a matter of putting the fields back together as they were originally. In fact, there's some redundant data that needs to be thrown out. Modern sets worth their salt understand this and do the necessary conversion (the feature is often listed as "3:2 pulldown detection").
Marketing gimmicks: DirecTV and Dish love to advertise "Blu ray quality 1080p" video. The reality is that 1080p/24 requires LESS bandwidth than 1080i/60! It's just a more logical way of transporting film material. There's nothing very revolutionary going on at all.
So why no 1080p channels? Most channels show mixed film and video material. Ofering 1080p/60 for sporting events is an entirely different ballgame that really would require a tremendous amount of bandwidth to do well. Some premium channels might be able to get away with a dedicated 24fps/1080p channel, they'd just have to show film material all the time.