International students can work while studying in Ukraine, there are no restrictions of any kind. Everything will depend on you, if you can both study (have good grades) and still find some time to work (may be at evening/night time, etc.), it is possible.
Of course the faster you learn the language, make friends, the higher are the chances to find a job. Also, if it is a university with a lot of foreign students, they probably can help you to find a job too, or at least give you good advice.