It won't grow significantly unless they do some massive marketing.
Fiat trading exchange is no good if no one knows it exists.

But they should market it ASAP so it attracts users before other exchanges catch up. This part is extremely important.
Once COSS amass users it will most likely keep them even if other exchanges implement FIAT as most people don't like to change what they are used to.
The second very important thing is customer support. They better get their shit sorted out and solve tickets really quickly. This will help people stay and the word will spread about how good COSS exchange is.
The third is trading API, upgraded UI/engine etc.

I hope COSS team know what they are doing. But I have not seen any marketing yet. Posting an update on twitter or something doesn't help much, you can't lean on the community to spread the word.