Yes, you can download a CSV spreadsheet of all the quizzes that have been assigned to a student. The spreadsheet includes all quizzes that:
were set by a teacher, and
were set in the current academic year (including ones with a start date in the future)
For each quiz, the report shows:
the quiz name
the subject
the start and due dates
the score of their best attempt
whether the student completed the quiz late or on time
how long the student spent on the quiz
How to get to the report
Go to Manage Students, Students, Classes and Years
Select the student or students you'd like the list for
Click "Download quiz list"
The list will look something like this: