Hey Pavlo,
This question is much more difficult than I originally thought! Here's what struck me from the current page on Wikipedia:
The ability of Gleditsia to fix nitrogen is disputed. Many scientific sources state that Gleditsia does not fix nitrogen.
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How this happens is not yet well understood but there have been some observations of nitrogenase activity in non-nodulating leguminous plants, including honey locust.
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It is not known whether the non-nodulating nitrogen fixation, if it exists, benefits neighboring plants as is said to be the case with nodulating legumes.
https://en.wikipedia.org/wiki/Honey_locust#Nitrogen_fixation
Sorry I don't have an answer, I just find it very interesting that there is dispute as to whether some legumes fix nitrogen. I never knew that.
I do want to share, however, that there is a sibling to Honey Locust, "Black Locust" which apparently does fix nitrogen. I hear Black Locust can be quite aggressive. However since it's native to my region (southeastern US), I intend to grow it.