The pencil tool that CtDave mentioned is possible, but it is not very useful for text. I don't know any other way to write on the PDF and so you might find it unacceptable. The issue of the browser window versus the actual Reader or Acrobat may also be an issue. Digital signatures are ideal, but for your application it is probably a bit hard to use since they have to be created for effective use and you may have customers who would not want to do that.
It might be useful to just open a PDF and see what you can do with the pencil tool and the signature tool to see if you feel it will be an issue. Trying it yourself may save you a lot of time asking the question in different ways here. Once you think you are looking at what you want, then some folks here might be able to help you further.