Yes, it can run along with antivirus with real-time protection (aka on-access scanner).
Not necessary to have on-demand scanner but if you want it.. it is OK since BitDefender 8 Free edition do not have real-time protection.
>>>>>The other thing is, does it even need AVG or Avast or anything else, can it protect your computer so long as you are faithful with scanning regularly and practice safe surfing?
Yes, you need antivirus like AVG, Avast or Antivir that has real-time protection. Don't depend with regular scanning alone. With the threats out-there, if you browse the internet regularly and if you are always online... you also need real-time scanner of antivirus.