After you bake eggplant, is it fine to not drain the water?
This is really about water content, not flavor. Eggplant contains a lot of water, and there can be plenty left after baking or grilling. If you then make a mashed/pureed spread like this, that water could make it a lot more liquid than you want.

That said, if you really thoroughly roast or grill the eggplant, you can get enough of the water out of it that you don't really need to drain it. If you prick a couple small holes in it, and bake for something like 45 minutes to an hour at 400-450°F (200-230°C), or similarly grill until it's well-charred, it'll probably be dry enough.

The exact details depend on the size of the eggplant, and what you're trying to make out of it.