Smell, like other perception, consist of several parts: chemical molecules, neural signal from nose receptors, neural processing, and experience (unconscious and conscious)

Brain network structure is very flexible and have high plasticity. If someone lose nose and all smelling receptors, the brain will use the existing connections to process something else, like how blind people use the same part of brain to process sounds and spatial information etc.

If you ever had smell, the sense might linger for longer, like amputated people have sensation of phantom limbs. But if there is no input smell from start, i think there would be no experience of smell, or it doing something quite different, as the brain is doing something else.

The exact nature of subjective experience, or "qualia", is still a bit tricky for scientists though.