Personally I think it absolutely should be uploaded at some point, preferably to an open repository, or one that has the endorsement of that field's community (see here for our own list of recommended repositories (https://www.springernature.com/gp/authors/research-data-policy/recommended-repositories). You can still have the data under a creative commons license in most cases if that is important, and it means more people will be able to use it. With the increasing number of data citations being used in scientific literature, it should no longer be the case that data has to remain closed until a research paper is published. Of course there is also an increase in 'data publications' where data can be described as a full publication, without having to have hypothesis testing, further analysis etc. Examples include BMC Research notes, Data in Brief and Scientific Data (full disclosure, I am employed by the publisher of two of those journals).
Definitely! There's evidence this increases the impact of the paper, and is good for reproducibility. Depending on the repository and journal in question, they should be able to help link the dataset and the publication where possible.
EDIT: Here's an example where authors have deposited the data after the study was published, and then published a data article describing it, a full year after the research article. Article Genetic determinants of sporadic breast cancer in Sri Lankan women