Kenneth ! This lens has its own servo AF-S "S" being the key letter ! And does not require an driver from the DSLR body . In most likelihood it should work ! Note that as an AF-S you will be in cropped mode on a DX sensor DSLR v/s an FX DSLR. Most consumer DSLR are DX format and don't use internal focusing drive pin.. Therefore limiting you to AF-S or AF-S Dx . Hope this helps ! Tried it on my kids D5000 and seems fine !
Kenneth, the 70-200 2.8 is a G-series lens and it will function on your D3200 with everything except the auto-focus. Your camera requires the use of AF-S or AF-I lenses to use auto-focus. Nikon's lower-end consumer camera bodies do not have the individual servo motors inside the body the way the higher-end bodies do and therefore they require lenses with the built-in servo motors. If you are willing to focus manually, then this great lens would work fine.