It may depend on the bulb. If your dimmer has a soft on and off feature where it fades the lights on and off as opposed to abruptly turning them on like a regular switch, there could be a slight delay before some bulbs will turn on. While most will operate fine with the soft on and off and changes to dimmer settings, there are some bulbs that have a built-in delay during those events and it may take a moment or so before they will turn on or respond to changes in dimmer settings.
To assist with bulb compatibility, use the Leviton LED Compatibility Tool