Can I see how much work is assigned to each person in a sprint?

Yes. By default, Scrumwise will automatically show you this in the Sprints page when it looks like it could be useful to you, like this:

You can click on a person to show the work assigned to that person:

You can configure when the assigned work should be shown, in your personal account page in the settings in Scrumwise:

When shown, here is what you will see: If the sprint is in planning, you will see how much work is assigned to each member of a team. If the sprint is in progress, you will see how much work remains of what is assigned to the person. And if the sprint has been completed, you will see how much work was assigned to the person in the sprint.