I think the answer depends on "who will be prioritizing the backlog items" (i.e. decide what needs to be done first). If this is a single person, then this person is the Product Owner for your projects, and you can have a single backlog will all items for all projects - or a backlog per project - and you select the backlog items from all projects when you plan a Sprint. In this case, Scrum "works" fine.
If every project has its responsible, then you're likely to encounter some troubles where each responsible will - more or less consciously - try to favor its project(s). IMHO, you'll need to have one Product Owner only with the authority to settle the priorities by arbitration.
One rule that shall be followed in such a context is to never change the Sprint content during the Sprint. If necessary, you can shorten the iteration to two or three weeks to lower the risk of having to add an urgent item in the current Sprint.
