You can get away with it on windows and even other platforms
You will lose all the ability to go crossplatform im pretty sure that is the case.
For example you can add a System.Image.Drawing reference and use the bitmap class and load huge images via system.Io using one of the stream classes, but that wont work on anything but windows. Further you have to load them into system.bitmap.color arrays then convert them to separate smaller mono game color arrays which is really actually simple you just cast the grba to rgba and then load them into separate textures using setdata<>
The upside to this is after you do all that you will realize your going to have to mipmap them and chop them up further for any real game and possibly for a image editor or any app as well.
But this is sort of a real problem just to get them in on any platform if they are large on file. Especially if you want to make a simple paint program in monogame that can load large images it was in xna too.