Regarding the implication, I think it depends on what we consider pipes to be for (it still has no wiki page). If it is for any cylindrical tube used to transport something from one place to another then yes, implicating drainpipe to pipes is fine. If it wants to be something more specific than that then it shouldn't.
Drainpipe and downspout are, for the most part, synonymous. Downspout is if anything a bit more specific to what NWF Renim described, and what the majority of the tag uses are for, but drainpipe is (in my experience) by far the more common word.
But the tag drainpipe seems to be being used for various things that are not actual drainpipes such as post #1746323 or various Mario pictures...