Easily, no. Technically, yes; however you would have to share whatever category they are currently housed within. This means if you created all questions within the "Default" category for the course, you could share that huge category of questions, but then the importing partner would have to hunt through every one of those questions to just find the desired quiz questions.
It is instead recommended to create a new category in your own question bank and then move those questions into that new category. This will allow you to export just the intended questions. See instructions here.