Can autofocus feature be used if I mount Tamron 16-300 for Nikon on Nikon D3300?

Yes, if that Tamron lens has a Nikon mount and has it's own built-in autofocus motor.

Contributor "Andrew" is correct! the Tamron lens will get very heavy around your neck if carried for 1/2 hour or more. I purchased a 18-200mm Tamron thinking I would use just one lens for pictures. But it WAS too heavy to carry for any length of time. I sold it within a month of purchase! I found the telephoto end of the Tamron very soft on 11x14 prints.

I now use the 18-55mm lens that came with my camera and added a 50-to-200mm and I could not be happier! My prints are sharp as a tack.

It's PZD, Tamron's equivalent of AF-S (built-in motor), so yes.

A point to consider, however, is that it's extremely difficult to maintain optical performance over a zoom range of this size, and the physical size and weight of this lens around your neck quickly becomes uncomfortable.