No. Safety 1st infant car seat bases are a convenience accessory, not a safety requirement for installation of the car seat.
In some situations (i.e.: challenging vehicle seat profiles, minimal spacing between front/rear vehicle seats, and traveling on an airplane), installation without the base may improve the installation and fit/compatibility with your Safety 1st infant car seat. Please see your model-specific car seat owner's manual for proper installation without the base.
Note: This includes onBoard 35, onBoard 35 Air, onBoard 35 Air+, onBoard 35 Air 360, onBoard 35 LT, Light ‘N Comfy 22 Elite, and Light n Comfy Elite models.
Note: When installing car seat without the base, a vehicle belt installation is typically required.