There is a wiki page that breaks it all down, the watering can does have an effect but it is only slight. There are 6 times throughout the day that the ender lilly can grow. On normal dirt and end stone only 50% of the time can it grow at one of these 6 times throughout the day, but on an ender core it can grow at all of the times, but it has to recieve a random tick during that time, and the watering can ensures it gets this random tick(it is possible for it to not get a random tick during it's available grow time) So you can't just sit there with a watering can and make it grow faster constantly, but you can use the watering can to ensure it grows when it is able to do so.
Quote from the same wiki page (further down):
- Every block update that happens while the proper "growth window" is active has a chance to trigger the next growth stage. Using something that triggers additional block updates, such as the Watering Can or the area-of-effect from a Sigil of the Green Grove from Blood Magic (not the effect from using it directly on a plant), can be quite useful to ensure that growth happens during every possible growth opportunity.