I am planning to buy AF-P DX NIKKOR 70-300mm f/4.5-6.3G ED lens for Nikon D3400. Can we take a good portrait from this lens, can we blur the background?
"Blurring" the background involves playing with the depth of field. Although I personally do not "favour" 70-300 for portraits, you can obviously "blur" the backgrounds using a aperture range of 4.5-6.3.
Good portrait not only means having great, expensive lenses in your kit. Sometimes, they do mean composing the portrait neatly and beautifully. I have seen people taking commendable portraits using a kit 18-55 lens.
I personally favour prime lenses for portraits. They pictorial quality the produce is awesome. For a good start, 35mm or 50mm primes in the budget ranges would be sufficient.
Such a lens is not perfect for portrait applications, but will do the job in most cases. It will certainly be a cost-effective option. You can find some exmaple images with blurred background in this review: http://www.kenrockwell.com/nikon/70-300mm-vr-afp.htm.
In fact, the blurring effect can be achieved with almost any telephoto lens. To increase background blurring, you should shoot from further away at longer focal length and make sure that the background is far away from the model.
There are a few cases where this lens will be limited in its usefulness:
1) If you want to shoot not just portraits but also upper body or full body photos. In this case a focal length of 70mm (for APS-C format) may be too long and you may want to go down to 55mm.
2) If you want to take pictures in dim light, for example inside and without flash. In this case you might want a higher-aperture lens. Those are, however, often much more expensive and much heavier.