As FastJack said, yes. Here's how it the rules work out:
... Elemental Strike enhances the effects of Killing Hands with an elemental effect (see pp. 164-165 of this book and pp. 154-155 SR4). The specific elemental effect must be chosen at the time the power is bought, though an adept may take this power more than once to achieve different elemental effects (only one elemental effect may be applied per strike). ...
[i[SR4[/i] pp. 154 - 155 ==
SR4A 163 - 165
... Treat Fire damage as Physical damage, but Impact armor only protects against it with half its value (round up). The fire resistance armor upgrade (p. 327) adds its full rating to the armor value.
Objects hit by a Fire damage attack are at risk of catching fire. Make a damage ressitnace test using the item's Armor x2 (see Barriers, p. 166) or just Armor if they are vulnerable to the effect (flammable material vs. fire, for example) ...
So, if you've got Strength 4 and use Fire Elemental Strike, you'll deal out 2P(f) (Str/2, modified by Killing Hands,
SR4A, pg. 196 and Fire Elemental Strike, above) as your base DV. Modify for net hits and all that happy stuff. It's also worth noting that with Killing Hands, Immunity to Normal Weapons is also out the window (
SR4A, pg. 196, Killing Hands) on top of the -half Impact from Fire.
Just hope the spirit isn't wearing Fire Resistant 6 (
SR4A, pg. 327) armor.