I'm sorry I cannot give you a more complete answer or an anecdote about trying this type of thing myself. But I would definitely say that anything i (480i, 720i, 1080i) is going to be problematic on a computer monitor. The i stands for interlacing and this is something (evil) that you see on televisions, not monitors. I would strongly encourage you to try a progressive resolution instead. However, if you can flip back and forth, don't take my word for it, look at both and see which one you prefer. At best, I would expect a flickering with an interlaced resolution, at worst a total distortion.
Has anyone tried what's out there for converting HD signals to something that a DVI computer monitor can handle? For example, can you get 1080i from an XBox 360 to display nicely on a computer monitor? What about the Playstation 3 at 1080p? Or even a Blu Ray or HD DVD player?