Yes, some people use 'leech' in a similar sense, but I suspect in many cases it was originally an eggcorn, because they knew the noun 'leech' and thought it seemed relevant, and they just didn't know the verb 'leach' or how it's spelled. Still, I would imagine it's older than the earliest citations here, since 1961 is fairly recent.
Either way, my point is that there is indeed a difference in meaning. The active sense, like 'suck,' makes sense in relation to a leech as used to drain blood, and the metaphor of rich or lazy people as leeches sucking money from society like blood is long established. The OED has actually chosen all its examples fairly carefully, since they all have a subject, a villain, someone or something actively drawing something else out or away. The brain drain is probably the weakest, but even there, people who know the context know that 'brain drain' is shorthand for the force exerted by richer countries (cities, companies, universities, etc.) that draws educated people away from poorer ones.
However, in the passive sense where there is no person as the subject, where the meaning is just 'drain' as an intransitive verb, the spelling 'leach' makes more sense -- as in the sentence given here by the original poster, where there's no active predator or parasite draining something in the sense of sucking or drawing it away, just a process like water draining through soil.
OT re #2: When you copy from a dictionary, please be sure to name your source.