Should I say
Does construction of railway lead to prosperity?
Or should I say
Does the construction of railway lead to prosperity?
Side note: If you are talking about railways in general, you should say "of railways", plural. If you mean one particular railway, like you have been discussing building a high-speed rail line from San Francisco to Los Angeles, then you should use the singular but you need the definite article, "construction of the railway". If you mean of a single railway, but you are not specifying which one, you should say "construction of a railway". Depending on context, there probably would be little difference in meaning between "railways" and "a railway".
But to your question: Either is acceptable. If you use "construction" without an article, you are referring to the idea of construction in general. If you use construction with "the", then you are talking about one time that someone did or will or might build a railway. Unless the context talks about one particular time that someone built a railway, "the construction" would still be a generic time, any time. So whether you say "the construction" or just "construction" you're still talking about the general idea of constructing railways, not one particular, specific time that someone built a railway.
Oh, in case that final point is not clear: Someone might well say that constructing railways in general tends to lead to prosperity, but construction of this particular railway line in this place in this year did not. Like to make it explicit, "Usually construction of railways leads to prosperity. But the construction of the Foobar Line in 1932 was badly mis-managed and poorly conceived and ended up seriously hurting the local economy."