It depends on which DTH you are using for the Sylvania buttons and for the Hue bulbs.
Are the Hue bulbs connected to a hue bridge? That’s the only officially supported method, for a number reasons.
If your Hue bulbs are connected to a Hue bridge and you are using the stock device type handler for the Sylvania devices, you should be fine: the official smartlighting feature should run locally, even if the Internet is down. But it all depends on which device type handlers you are using.
I’m tired today, so I will leave it to other people to explain how you can check for yourself whether your own account is set up this way.