This was sold to me as an Improved Celeste but the foliage looks more like a Bordeaux type leaf to me. What do you think?

Did you buy that as a plant or cutting? Definitely not IC. Leaves are similar to some good ones though.

I bought it as a dormant plant that was obviously started as a tissue culture.

Tami: That is not the Improved Celeste for sure. The leaves look very much like Stella. Thank you for sharing.

Best,
Tam

Temi,
Did you order it online? 
I would check what other varieties they have and try to narrow down the varieties with those thin leaves.
It seems it was mislabeled. 

Igor, that's all they had but I'm almost 100% positive it isn't Improved Celeste.

It doesn't really look like any type of Celeste. Too bad there aren't any ripening figs to help ID it.

Tami,
  What makes you think it was started as a tissue culture?  Is it the multiple trunks?
Note:  some of the online nurseries that deal in tissue culture plants (and may distribute to other nurseries) seem to offer Magnolia/Brunswick as one of their choices.  The leaf shape of your tree is suggestive of Brunswick, as is the slightly pink hue of the leaf stems and buds.  Note -- don't quote me on any of this as an expert, I'm just passing along what I think maybe I possibly learned a few weeks back when looking into some strange "creeping" figs at a nursery.  It may be a starting point for you, though.  (I'd love to learn from someone else that it is something more exotic!)
Jim

Thanks Jim,
I think we can all put to bed the idea it might be something great. Wouldn't surprise me at all if it is Magnolia/Brunswick in which case I want it in the burn pile.
I think it was a tissue culture because even when I got it dormant this spring it was very small and looked like a huge spider, lots of long spindly legs.

It seems it has a strong root system. Graft something nice onto it, it is going to be a win-win. You don't have to fight the gnats and will have several varieties in a pot.

I'll give that some serious consideration Igor, if any of the branches are big enough :)

The branches are perfectly fine. 
After your graft, you expect some active growth to heal faster. This might be better to do next spring. Several things will be better: the branches will be wooden, the growth is expected, easier to collect the nice varieties over the winter, warmer temps ahead in the summer.
The best time is when the fig is out of dormancy and starts growing. I also think it is better when the scions start pushing the leaves, just start them in a moss bin.
When they are ready, cut the bottoms off the way you like it and graft them!  
The success rate for fig grafting is quite high. Good luck!