I've ridden several centuries on my hybrids; I just did a week-long tour on one, riding between 55 and 105 miles on my riding days (I volunteered 2 days). I do have slightly smaller tires than the standard - but basically, get out there and ride on it and get in shape and yes, you can do it.
People who ride a lot of distance get tired of going more slowly and doing more work. THis is a special event. You will, I am sure, find a lot of other hybrids and mountain bikes riding right along with you.