If I have a plain-text field on a web form (not a file upload) inserting its content into my table, would it be wrong for me to set a mime type 'text' to it, or would it be safer?
MIME types is basically a way of saying "this string of bits should be interpreted/processed as X" so it's equally viable for files and transfers. The more common way of doing this for files is by file extension.
You seem to be asking "is software X doing anything special based on the mime type setting?" without saying what X is.
This totally depends on your application. MIME is made for and is most common for E-mail, but it's also common for the web (http) and in some NoSQL databases.