He used to walk along the alleys running in the shade of the old park's poplar trees.
The construction makes it possible that both he and the alleys might run in the shade.
To insert a comma after alleys would indicate that the person was running.
As it stands, the understanding is that the alleys run in the shade.
Many such statements are simply ambiguous and depend on the punctuation for guidance.
Take for instance:
He used to walk along the alleys lingering/resting in the shade of the old park's poplar trees.
Here, a comma before lingering or resting makes it clear that he is lingering or resting. But the punctuation without a comma implies that the alleys are lingering or resting, which is unlikely but poetically possible.
So the reader has to decide what you are trying to say. Much would depend on the context.
I don't think your example would be misunderstood.