It should be. However, not only is the number of Icons available hardcoded, but the initial Icons Types are hard-coded as well.
It could possibly be expandable to being able to ADD to the existing Icons.tbl (via an -ico.tbm) but you wouldn't necessarily have the flexibility to alter the retail ones at all.
As for Species/vs Icon, you can use any briefing Icon you want already independent of the Species. I can make a Demon show the Hecate if I wanted to, based on using the Icon index (I think, not that I have actually tested this, mind)
If it turns out that you can't, then yeah, in addition to expanding the Icons.tbl, adding "Species Free" ability to it would be nice.