There are a number of written instances of (someone) took transport to (some destination), where it's important to note there's no article. If you look at the dates in that link, you'll see most of them are quite old.
Also note that in such contexts, transport is effectively equivalent to transportation. It's more of an abstract than a concrete noun - referring to a means of travel, rather than a specific "conveyance" (a physical thing in which passengers / cargo are transported).
You won't see the usage a transport (with an article) very often at all. It's sometimes used (mainly in military or technological contexts) where the fact of things/people being transported is more relevant than the actual thing they're transported in/by.
OP's example context (Sam took a transport to the house) is completely non-idiomatic, and always was. Without the article, it's "just about" valid, but it sounds like something out of a Dickens (Victorian) novel.
Note that it wouldn't be unusual to say Sam arranged transport to the house even today, but that wouldn't necessarily mean that he actually made the journey at the time (perhaps he made travel arrangements for someone else, or for his own future journey).
To sum up, Sam took transport to the house is technically valid (with the sense of made use of a transportation service / type of transport), but you can't use a transport in such contexts as a generic reference to an individual conveyance / vehicle / vessel used to transport something.
