Short answer: Yes.
Long answer: Some people used to say you could not, but grammar books now say you can. The controversy used to be about whether hopefully is an “independent comment” like finally, actually, regrettably, fortunately, and many other words. These words act as asides to the reader to indicate the writer’s opinion or attitude about the entire sentence. If you need a more technical term, they are “sentential modifiers,” adverbs that modify the entire sentence.
If you are curious about some of the players in the controversy, they are The Careful Writer by Theodore Bernstein, The Chicago Manual of Style, and The Gregg Reference Manual. My opinion, stated above, agrees solidly with The Gregg Reference Manual. Chicago says that the usage I cite above is “here to stay,” but snips, “But many careful writers deplore the new meaning” [emphasis added—could this be a nod to readers of Bernstein?] Bernstein has not been updated, fyi, since 1965.
Yet another voice in the squabble is The Oxford Dictionary of American Usage and Style, by Bryan Garner. The advice here? All the controversy has ruined this word. Never use it at all, because no matter what you do, someone will think it is wrong.
Meanwhile, Merriam-Webster.com utterly dismisses Bernstein and all critics and solidly supports the use of hopefully as an independent comment.
So there you have it. My vote is to use it until people get over its history. After all, most people have long forgotten the “impact” wars of the late 1980s. But on the other hand, I recently encountered “impact is a noun only” still alive and well in the style guide of a large organization. Ultimately, I guess, each writer must make up their* own mind.
*Watch for a future article on the use of their.