All blackbody emitters emit in all bands (in practice, since nothing is a true black body, it's concentrated into certain bands). The curve is like this:
A couple general notes:
1) The falloff in output is much faster for frequencies over the peak than under it.
2) The location of the frequency peak is relative to the body's temperature - which is why room-temperature objects tend to emit mainly far-IR, hot objects tend to emit mainly near-IR, and plasma like the sun tends to emit mainly visible light. It's also why once objects get hot enough they seem to start glowing in the visible spectrum - technically, everything glows in the visible spectrum, but the amount of radiation emitted is so weak as to be irrelevant. It's also why they start out as red, move to orange, yellow, then ultimately white with increasing temperature - it's the combinations of their emissions integrated over their (approximate) blackbody curve. You never see, for example, "green hot", because by the time the peak is around green there's also so much contribution from yellow through red and a bit of blue that you just see white.
3) The output rises a *lot* with temperature - more specifically, relative to the temperature to the fourth power. Which is why a steel wire heated as hot as you can without melting it doesn't make a good light bulb, but doing the same with a tungsten wire does - the higher temperature makes a huge difference.
As for the usefulness of anything for communication, there's several factors.
1) How much natural interference will it encounter (aka, how much noise will be in with the signal)?
2) How much will it be attenuated (absorbed) by e.g. the atmosphere, vegetation, human structures, etc?
3) How directional are the source and receiver?
None of these ever pose fundamental, 100% barriers. But any of them can make a given means of communication impractical for a given task.