Yes, you can, since Vim has special regular expression atoms for marker positions, and the beginning and end of visual highlighting are marked with '<and '>. Since there are atoms to include / before / after the label, we need to combine them to cover the entire range of selected lines:
At the beginning of the selection |after the start of the selection and before the end of the selection |at the end of the selection.
To limit the search to the current file, a special keyword is used %.
:vimgrep/\%(\%'<\|\%>'<\%<'>\|\%'>\)FOO/ %
source
share