Hellgate Weapon Modifications

From this post, it seems like there are two types of attacks for the same element. Damage and Special effect strength. The post does a good job of explaining, but in summary.

Elements add both damage, and ability to proc special effect:
Physical - Stun
Toxic - Poison
Fire - Ignite
Electric - Shock
Spectral - Phase

Assume you have a sword that does 100 Physical damage with 100 Physical Attack Strength.

If it has 4 mod slots and you put in:
+10% Toxic
+10% Fire
+10% Electric
+10% Spectral, you now have a sword that does:

100 Physical damage, 100 Physical Attack Strength
10 Toxic damage, 0 Toxic Attack Strength
10 Fire damage, 0 Fire Attack Strength
10 Electrical damage, 0 Electric Attack Strength
10 Spectral Damage, 0 Spectral Attack Strength

So basically, against some monster with 100 resistance to all elements. You have a decent chance to stun, and basically 0 chance to poison, shock, ignite, or phase. But you still do the elemental damage.

But what if you add a mod that increased Elemental Attack Strength but the weapon doesn't actually do Elemental Damage of the same category?

Like If I put a +100 Fire Attack Strength mod into the base sword, will it have a decent chance to both stun and ignite? Or do you have to actually do fire damage as well to proc the special effect?