You are asking if a computer that is less powerful and has lower resources can run apps at the same speed as a more powerful one. Of course not. The question however should be if it runs them at good enough speeds, the answer is yes. But more importantly, thou, is not how fast Parallels runs, is how fast the Guest OS runs, and this is very much dependant on the Guest OS, is it Windows, OSX or Linux? is it Windows XP or 7/8.x? Is it 32 bit or 64 bit? 32 bit versions are more adequate if the total physical RAM does not exceed 4 GB, or else you might experience some occasional slowness.