I'm dealing with this question for a (fan fiction) Role Playing Adaptation I'm working on. I've concluded that the books are deliberately fuzzy on whether smugglers (and rogue houses) have access to illegal interstellar transport. I'm restricting this answer to the Corrino Imperium Period. Based on technology and culture I have concluded the following:
The legacy Faster Than Light used at the time of the Jihad era prequels is too slow to be useful for other than short runs between neighboring systems. This technology does not require a prescient navigator, and would thus be the more common illegal technology. For long hauls just the time involved would make it more expensive than typical guild rates for everything except military transport, and no noble would want their fleet stuck in tranport for months during a conflict.
Holtzmann tech is widespread. with good engineers jury-rigging foldspace wouldn't be hard. Without a prescient navigator Dune canon is very consistent that loss rates run about 10%.
Since no illegal tech available to smugglers can compete with the guild for long range transport, the cost of guild sanctions (disruption of heighliner service) for being caught using illegal transport could destroy the economy of a world.
Out-Freyn worlds are not subject to the Guild Monopoly, and would presumably have to use legacy Lightspeed.
There is a passage in Dune where Jessica wants to become friendly with smugglers because she believes that if they need to run that the smugglers can get the Atriedes off Arrakis if the Atriedes cannot use a Heighliner.
Which doesn't answer the question of how much smugglers depend on their own illegal lightspeed vs paying the premium to the guild for no questions asked service. It would seem that smugglers usually pay the premiums and bribes to customs and the guild. Customs evasion would seem to be the more pressing advantage of faster than light. Paying double the normal rate to hop a heighliner is probably still a lot cheaper than running illegal tech.