I'm not sure what the expectation is but I've never played a Church Organ before. Assuming i could figure out the right stops to get a good sound, would I be able to play the piece and have it sound good, without using the pedals?
That's a really big assumption. If you show up that morning and try to figure it out on the fly, I would say it is simply impossible.
On the other hand, if you have a bit of time to practice AND the advice of an experienced organist, you can probably play one simple piece with a good sound.
Organs aren't all the same. Is it electronic or pipe? Does it come with presets? What are the couplers? Most organs will couple the pedal TO the manual, some will couple the pedal FROM the manual, very helpful for inexperienced organists.
Or would the bass just sound way too thin?
Depending on the stops available on the manuals, probably the bass would be fine. I did a number of church jobs without using pedals when I started. The organ in that church had stops you could choose, or it had some buttons with pre-set combinations of stops. As I was learning I relied heavily on the presets.
Bottom line though, IMO there is no way to make your keyboard sound anywhere near as good as a real organ, even an electronic one, and it is worlds away from the pipe. Remember that this is the single most important day in the bride's entire life, and it will be on video forever.