No, all vehicles that are not exempted are subject to a valid vignette from the moment entering Slovakia.
Cameras will scan the license plate right at the border and check within the toll system. Violations lead to heavy fines.
You can order your Slovak e-vignette comfortably here.
Related articles:
What vehicles need a Slovak e-vignette?
What happens if I drive without a Slovak e-vignette?
Which roads require a Slovak e-vignette?
How is the Slovak e-vignette checked?
Can I drive into Slovakia without a valid e-vignette if I avoid motorways?