Quest Web Parts are available for use in SharePoint Online/BPOS-D (2007 version). However, the process involves completing a High Level Design Document (HLD) for each customer; whereby, the customer is essentially asking Microsoft to make an exception for a "No Third Party" software rule that Microsoft has with its BPOS-D environment. The process is quite lengthy and I cannot recommend that a customer goes through the process because of the length of time to get through the process.
Quest will be putting out sandbox versions of its Web Parts that could be used for Microsoft Office 365. That will come later this year.