Can I delete a team member and not lose the time tracked on projects?

No, you cannot completely delete a team member, since the tracked time on projects will also be deleted. Though, you can lock a member, so he won't have access to your projects. For this, perform the steps below:

1. Go to Workspace and click Members. 
2. Click the menu next to a required member's name and select Lock Member. 
3. The member's status is changed to Locked.