Nope, there is a distinct differance between "заканчивать работу" and "заканчивать работать".
Imagine you come and see your friend working. You want your friend to go with you and you say:
- Заканчивай работать и пошли со мной. Here you mean stop the proccess of working and come with me.
Your friend replies:
- Сейчас не могу, мне нужно закончить работу. Here he means that he can't go with you now, because he needs to finish the work he's been doing.
In short, when you say закончить работать, you mean to stop the proccess of working
When you say, закончить работу, you mean to finish the specific task you've been working on.