Given the fact that waterfall has proven its mettle in time and again if done properly, but it has its shortfall too ,some time because of the rotten mindset of the people in the system
it becomes a overkill.Waterfall has its strengths which are well established and no doubt that Agile is gaining acceptance since it can accommodate change better. . Can they co-exist?
I think I have mentioned my wife's company as a good example of a relatively successful hybrid. As others have also noted, any reasonable process can be made to work given the right people, motivation, attention, and execution. What differentiates agile and traditional most of all are, IMO, for the most part, the intangibles, of which I will refrain from giving specifics here but will refer you to other recent topics in this forum to peruse and figure out yourself.
I was trying to find that post about my wife's project but it's lost in a big thread somewhere. Anyway, what I was referring to is a project where my wife works that touts itself as being an Agile/Scrum project. As Agile/Scrum goes, it's highly questionable. They are using the terminology of Scrum such as User Story and Scrum Master and Backlog but they are doing things in a highly traditional manner, with silos for developers, business analysts, testers, and very little collaboration going on in the actual writing of the code. Things are still getting done the traditional way where business analysts write out the specs in the form of detailed User Stories (which are not supposed to have a lot of details) - developers waiting for BAs to hand them the specs (the User Stories), and then handing off the finished programs to QA/Testers when they're done with development. This is not what Agile development is supposed to look like. However, they still make it work and they're happy to call themselves an Agile team.
They still have lots of bugs, and lots of communication and collaboration issues, and other things par for the kind of course that they have made for themselves. However, they are on a shorter release cycle (I think once a month or every 6 weeks, if I recall correctly) than the rest of the bank which does releases on a quarterly basis (every three months) and not every project actually does a release every 3 months - that's just the window in which they coordinate releases for anyone who is ready to do one.
So, to answer your question, yes, agile and traditional practices and methods can coexist. I also think that sometimes that's the best you can do in some situations. As I said above, success really depends on having the right people working on the project, with the right motivation, dedication and attention to detail, and good execution. Whether they doAgile or Traditional or a mix of both, as long as they can get the work done, deliver, and maintain a reasonable pace, it's all good. The question is, how can you make it better?