Do acids react with neutral salts?
Neutralization is a reaction between acid and base which results in the formation of a salt and water.
When you have any ionic compound and dissolve it into water, dissociation occurs.
This means that you get a solution of ions.
So if you dissolve acids, bases or salts into water, you end up with a mixture of ions.
Then, more things may happen or not.

In the case of the given reaction, you will get a solution with:

$\ce{Na+ + Cl- + H+ + SO4^{2-}}$

If the system is closed, nothing will happen.
But if the system is open, then $\ce{HCl}$ will evolve because it is a gas.
Since the sulphuric acid is very polar and a liquid, water is not even required.
This is, in fact, the standard procedure to prepare anhydrous HCL in the lab. Just drop $\ce{H2SO4}$ on $\ce{NaCl}$. It must be said that $\ce{NH4Cl}$ works better.