Keeping this in view, can you use a 250w HPS bulb with a 400w ballast?
The ballast is "capable" of pushing 400w but if u put in a 250w bulb, then the ballast/bulb should have no prob as long as you don't go over what the ballast is capable of!
In this manner, can I use a 250w bulb in a 600w ballast?
YES ITS FINE!!! I would not however ever suggest putting a 250w bulb in a 600w ballast, it will blow and also potentially explode!!!
No it will not produce 600 watts, thats why they make a 600 watt ballast. Spend what you can here, it is a worth while investment. It probably will light the bulb (magnetic ballast, digital i question), and there is no reason it should shorten the ballast life, the bulb however it most likely would.