"does the intended purpose of a language have any bearing on how it's actually used, or whether it becomes popular?"
I don't think the intended purpose of a language has much bearing on its actual use and popularity: There are some great languages that were designed from the start to be innovative, flexible and versitile, but never became that widely used or popular except in very specialized vertical markets - for example Eiffel. OTOH, Basic, Pascal, C etc etc dominated the landscape for years although they were designed originally for limited, specific purposes.
IMO Marketing/financial and support considerations have always played a major role in the spread and extension of certain languages. For example: Borland comes up with TurboPascal and packages, markets and supports it. MS comes up with C# and packages, markets and supports it. As a result, these languages became popular, third party tool industries sprung up and more and more developers and enterprises jump on the bandwagon.
But for the last few years, openSource languages and tools are changing the dynamic and languages now become popular based more on 'merit' than marketing - for example Ruby, Python and Perl. But that's not because of the 'intent' of the inventors so much as the language's built in potential for extension and expedient usage.