In general, yes. Any additional process step adds a cost, but based on my experience, the primary cost driver is the number of lamination steps. If you can keep your PCB to a single lamination step, that would be ideal cost wise. If you have to use buried vias, it would be best if those buried vias occur across a single core since those can be drilled and plated prior to any lamination step. A multicore buried-via will require an intermediate lamination step before the drill. Some blind vias can be accomplished using controlled depth drilling after the complete lamination assuming the layer spacing is adequate, so a controlled depth blind via may not add much cost.
If you can design your board to use only traditional vias, with no blind or buried vias, that would be the lowest cost route. Depending on the complexity of your board, you may not have a choice however.