no, you would just get 110:12 and then back 12:110.
The first transformer goes from mains to the 12V (in this case 110:12).
Then you have to get from 12V to 220V. In which case you need either 6:110 or 12:220 (only the other way around, since you're using step down transformers backwards)
The ratio 110:6 gives you a multiple of 18 1/3. So if you're feeding 12V into that, you get 220VAC.
If you use 110:12, you only get a multiple of 9 1/6, which would only get you back to 110.
I've never been great at describing things verbally, maybe I should try graphically.
Daniel