Can a blunt knife be sharpened?

You will not be able to sharpen it with a steel as per Ching Chong's answer. You will be able to sharpen it with a couple of sharpening stones. If the blade is totally blunt you will need a reasonably coarse one to bring the edge back, and a finer one to refine the edge. Then you can strop it on the steel or the back of a leather belt to remove the burr.

However, unless you have experience in sharpening, the results will probably not be worth the outlay for the stones. That is, unless you use these knives for practice, then invest in a decent one afterwards. There are any number of videos on YouTube showing you how to sharpen kitchen (or any other kind of) knives.

Very blunt knives need to be reworked by stone or sandpaper

The edge on a very blunt blade will have folded over itself and lost a lot of its proper crystal structure. It's also likely to have lost a lot of its bevel geometry too, so the edge won't be "straight" longitudinally.

Your best bet would be to invest, just one time, in sending it in for professional sharpening, then keeping it sharp using leather stropping or a honing rod.

Don't try to sandpaper it as there is no way to ensure proper bevel geometry with sandpaper without some professional equipment.

And...sending the knife in will be cheaper than buying a set of wetstones (which most folks don't know how to use properly anyway).

Here are some images of folded and blunt edges:

Do you mean by "sharpening steel" a honing steel?

_{source: Wikipedia Commons; by Donovan Govan.}

A honing steel is not intended to sharpen a dull knife but only to straigten a skewed blade [1]. (Exception: a diamond honing "steel" but I think it it still not intended to be the only tool to sharpen a completely blunt knife, [2])

If you want so sharpen you knife in a cheap way: Use sandpaper instead of a sharpening stone. :D

1: A: How should I care for my knives?
2: A: Does a sharpening steel ever need to be replaced?

You can always sharpen a knife. The point at which they are two far gone, is when there isn't any steel left. That would take an awful long time though. You (or whoever sharpens it for you) will just remove enough steel so that it is sharp again.

A ceramic wheel sharpener (the kind that needs to be filled with a little water before using) is probably the most practical compromise for good results with little potential for worsening the blades. These aren't very cheap usually but worth the time and frustration saved.