I am trying to install Android 4.0 on a tv box. I just need to know whether Android 4.0 will have the HDMI drivers.
It depends on how the Android image you're using was built. When you build a ROM image from the Android sources, you set what drivers are included in the image, according to what target hardware you're expecting to use it with.
If you got the Android image from the manufacturer of the TV box, it should have drivers for all the hardware in the device. (At the very least, it should say if anything is missing.) If you're using a third-party image that was created for that device, again, the author should tell you which hardware is supported. If you're using a third-party image that wasn't created for that device, it probably won't work at all.
If you're building your own Android image, then you should look in the sources you're building from, to see if the HDMI driver is included; if you don't already know how to do this, you probably shouldn't be trying to build your own ROM.
You might also find Can I install Android on my non-Android device? useful reading.