In Australia where your profile indicates you are located, Nikon only offers the D3400 in kits with an 18-55mm lens with the AF-P DX NIKKOR 18-55mm f/3.5-5.6G (non-VR version). What the salesman is telling you seems to be true, at least with regard to the lens, in Australia. The bit about VR no longer being needed "because the processor takes care of much of this function..." may be a bit more of a stretch. If Nikon has modified the way their camera bodies, particularly the D3400, process images to reduce blur they sure haven't touted it in any of their promotional materials.
If, however, one were located in the U.S. your question would have an entirely different answer.
The kit lens included with the Nikon D3400 in the US is the AF-P DX NIKKOR 18-55mm f/3.5-5.6G VR. The 'VR' at the end of the lens' name stands for 'Vibration Reduction'.
The non-VR version of the AF-P 18-55mm is not listed in any official D3400 kits at the Nikon U.S. website. The non-VR versions of the Nikon AF-P lenses are marketed by Nikon in the U.S. to be used with older bodies not capable of turning VR on/off via a menu selection since the AF-P VR lenses do not have an on/off switch of VR on the lens¹. The D3400, at least the version of the D3400 sold in the U.S., has the ability to control the VR on AF-P lenses via a menu item.
If you were in the U.S. and a salesman is trying to sell you an 18-55mm lens with a D3400 that is not a VR lens he is either:
- Ignorant of what he is selling
- Trying to sell you an old (pre-2007) lens or a cheaper non-kit non-VR version of the AF-P 18-55mm with a new camera body, probably for the suggested price of the newer/higher priced lens.
In which case run, don't walk, to the nearest exit of whatever store this salesman works.
¹ Please see Thom Hogan's comments in this revue regarding VR vs. non-VR versions of AF-P lenses.