It's a difficult question to ask... and one that sometimes is only elucidated by reading Japanese sources (read- Non English).... Most English definitions, I'll use wikipedia as a source of possible (mis)information, yet I am fond of it's Japanese version for elucidating what the English versions leave out.
The Geisha of old, did in FACT work in what would be considered to be called the "red light district".... they made their money by entertaining men. You may or or may not be acquainted with the term Mizu Shoubai, or in English, "Water Trade"... there is some contention to the origin of this phrase, if it deals with the onsen (hot springs/public baths) where it originated, or the flowing nature of the business... but by and large, it is still prevalent today, and though some see it much like prostitution, it is, selling company to men, for money, for quite expensive sums, I'll leave that up to you to research.
Undoubtedly there were Geisha who were not trained specifically to be elegant, and not specifically to be entertainers, popular culture films such as the most recent iteration of Zatouichi make such claims, and I think your responses from the Japanese may be different (I am not, of course Japanese, but well read on these subjects.... Asian Studies major... blah de blah..) then those of non-Japanese origin.
I think personally, that of course there were many geisha who operated in a manner, indebted to their mama-sans to entertain chiefly, and wed, and provide sex, lastly... The idea of the untainted woman should be of some familiarity to you... Memoirs of a Geisha (Sayuri in Japan), is not the best source on the subject but it does elucidate some things, frankly a little less than what Zatouichi inevitably elucidates but does so, nonetheless.
Of course, like Mizu Shoubai, it is entirely up to the "peformer" as to the extent of IF they do provide sexual services to the customer, of course, with geisha, this would make their perceived worth lessened, so, perhaps it is not as common... not so much in Mizu Shhoubai, where men pay for the company of women (I have been), there is no touching, there is no contact, and depending on the establishment, there may be no impetus for the hostess (girl) to initiate any sexual contract--- though it is still possible.
That is my point about geisha, the possibility of contract.