Does VLS limit a submarine's diving performance?

Does fitting VLS reduce a submarine's maximum depth or diving speed?

Not significantly; the main constraint is that the submarine must rise to a suitable depth for missile launch.

VLS uses self-contained modules within the submarine's hull. An analogy with external Second World War torpedo tubes separates the launcher installation from the boat's general diving performance. Missile firing has its own depth restriction: the submarine must rise to a suitable launch depth while remaining submerged. After firing with the supplied targeting information, it can descend again and leave the area.