The short answer is: you can use them; it's likely that you'll be understood; some people will think you don't know English very well.
Longer answer: my first instinct is to say, no, those uses are unacceptable. It's true that those verbs are used intransitively, but not in those ways.
"He imports" does not mean he is imported, it means he engages in the business of importation. Products cannot do any importation (unless the product is an importing robot).
"She checks in" means she checks herself in somewhere. Luggage cannot check itself in.
If you want to be safe, stick with the established usage: luggage is checked in, products are imported.
On the other hand, native speakers do not always follow these rules. Recently, I have noticed native speakers using an almost identical phrase as the one you've proposed. Instead of saying "it will be released" people are saying "it releases."
In fact, by the time it releases on Netflix, it’ll have been roughly three years since we first learned about the series
("What's on Netflix")
What time does Stranger Things season 3 release on Netflix?
Eazy didn't stop there, as the "No Limit" rapper also put his hoop dreams on display with Tyga in the "Bang" visual, which also released on Thursday (Aug. 22).
This non-standard usage perfectly mirrors your propositions. The album releases on Thursday : The product imports mainly from South Korea.
Hearing release used intransitively sort of makes me cringe, but clearly some people find it acceptable. Those people would likely accept "the product imports" as well.