Short answer: No it doesn't, and no it won't.
There was a recent patch fix that had to do with the intro screen not fully using the higher resolution window. I don't know if it will do 1600x1200 (sidebar
WOW! What kind of monitor you run that on? Big screen HDTV?
) since my own monitor will only go up to 1280x1024. But this has no effect on the actual game itself, only the intro screen.
It's not the simple matter that you suppose to make the game handle the larger screen. If it had been written that way to begin with, perhaps, but all of the visual game elements in Se4 are bitmap files. There are two sets of game screen elements to handle either 800x600 or 1024x768 size desktops. Changing that at this point would require either a extensive rewrite, or creating a whole lot more bitmaps. Neither is going to happen since we have most likely seen the Last patch for SEIV.
SE5 will use 3d rendered graphic elements, and I expect will be coded to handle the larger resolutions.