That's a good thought. This was someone else's thought as well.

Here are my thoughts:
I don't have any specific knowledge of Coinbase's backend, but I suspect that Coinbase purchases are routed directly to GDAX. In other words, Coinbase's backend is GDAX, and Coinbase acts more as a broker. Coinbase exchange changed to GDAX in 2016. Source: https://blog.coinbase.com/coinbase-exchange-is-now-gdax-adds-ether-trading-a82cc628aa79

Given this, I wouldn't expect the volume on Coinbase to be separate from what we see in the trade history occurring on GDAX. This is just speculation though.

This is stated in the trading rules:
“3.4 Coinbase, Inc., which owns and operates GDAX, also trades its own corporate funds on GDAX. “

Here is a another reference:
What is a broker-dealer? -