Yes, as long as no toll roads are used, no e-vignette is needed.
You can learn more about what roads require an e-vignette here.
Related articles:
Which roads require a Slovak e-vignette?
What happens if I drive without a Slovak e-vignette?
How is the Slovak e-vignette checked?
Where can I buy the Slovak motorway e-vignette?
What different types are available for the Slovak e-vignette?