Oh dear
YES you CAN use a smaller normal map with a larger texture,
<span style='font-size:9pt;line-height:100%'>AS LONG AS THE RATIOS REMAIN THE SAME</span>. I.e. if you have a 1024x512 texture, then the normal map needs to be 512x256, or 256x128, or ofcourse 1024x512.
[Edit to add] Although this brings little to no benefit (aside from saving a little bit of gfx RAM) so theres really not much point. [/Edit]
And lets not even begin to go down this "Bump mapping Vs. Normal mapping" road (again, for the 4346456456 gajillionth time) ArmA supports a very specific set of
normal maps, as listed on the wiki:
# _NO - normal map
# _NS - normal map specular (with alpha)
# _NOF - normal map faded (mipmaps fade the texture in distance, usefull for terrain)
# _NOHQ - normal map high quality
# _NOVHQ - normal map high quality
However, technically speaking, normal mapping is a variation of Bump mapping. But for simplicities sake, lets just call it "Normal mapping" since thats the standard used throughout the engine.
What you describe as the "high polys model- low polys model method" is not called "bump mapping" but is a method for
generating bump (or more usually) normal maps, by using the details of a high-poly, high-detail model to generate a normal map for a lower poly mesh.