If they indeed were planning to list in there (which i doubt), they would only need to code a bridge for that, many projects have done that so it's not a big issue. And even if they plan to list, i would think that this would be counted as security, i mean this is hardly an utility token, thus preventing the listing.
I don't really expect CUR to be able to register on Binance DEX, aside from the inconvenience of having to change the network to BEP2, the daily volume of Binance DEX is not too large, I rather hope that CUR can be listed in a better exchange without having to change networks