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The first modern stick grenade appears to have been the British No. 1, developed in 1908. It had an impact fuse, and was a liability in trench warfare, being replaced by the time-fused Mills Bomb.
I can't find any reference to stick grenades in the black-powder era.
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Grenades have been around since the 13th Century. China, especially used gunpowder in their grenades, which some people argue was the first grenade. Stick grenades were first introduced during World War 1 by the Germans, which was lighter, cheaper and more convenient. This Grenade revolutionised the future of grenades.
There's no proof that stick grenades existed before the Model 24 Stielhandgranate but it is very possible there could have been similar designs in China from the 10-20th Century.
Another grenade used developed was the Russian-Made RGD-33 and the British No. 1 grenade also used in WW1.
The Answer to your question is yes, probably, as the Stielhandgranate was the first documented and used stick grenade.
EDIT: The British No.1 grenade was, at its time unreliable and little known. Production for it only started in WW1, which makes the Stielhandgranate the first used and reliable stick grenade.