It should cope in my opinion, the only concern I might have is that to a degree it depends on the optimum resolution for the monitor and if you then run the graphics card at the optimum for the monitor then it will put it under pressure a bit, this might be ok for many things but if you play games with it the graphics card might struggle.
Its a huge jump from a 15" to something like a 24".
What I would do is try it and see. You don't have to run the monitor at the optimal settings if you don't want to. Try it.