It depends if you have a small attic along the ridge or each of the rafter spaces acts as an individual air passage. I slightly modified InterNAHI drawings to explain three scenarios.
If there’s no open space (small attic) between the roof’s ridge and the top of the ceiling ONLY the rafter spaces that include 3 new roof vents will be ventilated (assuming that the insulation and all soffit vents have been properly installed).
If this is the case and you are experiencing cold winters there’s a chance that your roof decking will eventually be mold contaminated due to moisture buildup and lack of ventilation in several rafter spaces. If you have some open area under the ridge that allows for air flow between the rafters, those 3 new roof vents might be sufficient.
If there are ventilation problems and you have no access to the rafter cavities you may not be able to see anything on the exterior and nothing on the interior, at least for some time. Everything will depend on the temperature, humidity, and extent of the ventilation problem.
However, if the ventilation has been compromised (with the ridge vent removal) and you have cold winters, you may start noticing moisture stains on the ceiling (various areas, most often along the ceiling top section and along the ceiling – wall seam, above the windows), condensation dripping from the soffit vents, icing patches on the ceiling surface.
Look at the drawings and let me know if you have other questions.