Personally, I don't foresee why you couldn't use Bitdefender, VoodooShield, and Zemana together. I do agree that you may see a significant slowdown in your computer with everything running in real time. I would side with others in having Zemana being turned off for real time - use it as an on demand scanner.
Depending on how strong your processor is you shouldn't see any massive slow down, but you will notice some decrease in speed. Like
@ForgottenSeer 58943 has mentioned there can be some instability - hence the reason why I do not use Bitdefender due to some of the instability issues. Never-the-less, the software itself together is all great. If you take a look at my security config you will see that I use VS real time, Zemana real time, and Norton real time. I do not see any slowdowns with my applications. Sure it may take my computer a millisecond longer to initiate everything at start up, but that is very small.
Hope this helps!
Brian