Once LN gets underway, this volume might even drop. That might actually be because Bitcoin's flexing its strength...
What I've been always interested in is what is the share of such exchanges in the overall Bitcoin trading volume. Although it's obviously impossible to pin down the exact percentage, maybe there is a chance to evaluate it at least approximately. No doubt there are many of p2p/off-chain transactions happening regularly, but I personally think that their volume can be negligible if compared to the known to everyone over 3 billion USD Bitcoin's daily trading volume.
I'd like to emphasize that what is interesting here is the volume and not the number of the transactions in question. It's a known fact that gambling sites, for example, process millions of off-chain transactions daily, but I think that their overall volume is not that big if compared to 500k BTC or so, shown on CoinMarketCap.