Ionic liquids normally have conductivities below aqueous electrolyte solutions, around 10-3 S/cm. They can conduct electricity and if that's the only essential property for the application you have in mind, they should work.
The best conductivity of an ionic liquid ( http://myweb.wit.edu/sandinic/Research/conductivity%20v%20concentration.pdf ) i.e. 861,000 micro mho/cm, corresponds to a resistivity of 1.16 10**-2 ohm m. It can be compared to 1.59 10**-8 ohm m for silver.
Thus silver conducts 730,000 times better electricity than 30 weight% HNO3 in water. An order of magnitude of 10**6 for the ratio between the conductivity of a metal and an ionic system can be kept in mind.
This can be understood by the fact that the ions hare heavier than electrons (minimum 1830 times) and that the ions have a very larger size than electrons (except H+). So ions put in movement by the electric field are slower and will have many collisions with the other atoms while electrons can travel several interatomic distances before being scattered by coliding an ionic target.
beg you pardon, HNO3 in water is not an ionic liquid, but just a base dissolved in water. Ionic liquids are both ionic and liquid without the presence of an additional solvent, such as water.
You may need to use a specific cell for highly viscous samples (for example we used Crison 50 73 titanium cell). It is very important to accurately determine the water content of the IL (and possibly to avoid environmental moisture absorption during measurements ) since even small amount of water could greatly its conductivity. Temperature is also to be controlled since ILs viscosity (and consequently conductivity) could significantly change when varying this parameter.