Will tariffs affect the price of contraband?

Yes.

Contraband includes products that simply skirt export/import controls.

One of two things may happen:

1. As demand for smuggled products increase, price goes up because demand outpaces supply.
2. Smuggling becomes popular and the market gets flooded with contraband. It causes prices to go down.

#1 is probably more likely unless enforcement isn't prioritized.

#2's likelihood increases when the import controllers are corrupt and susceptible to bribes, because they can look the other way as large quantities of goods are smuggled across a border.

These are not the only possibilities, but their examples of things that have happened at certain times in history.