If it's not TCP, but it is Wi-Fi, you should be able to capture it; the capturing is done at the link layer, so it should see all Wi-Fi traffic that it can receive. It can capture UDP traffic (which has no 3-way handshake), and it can even capture non-IP traffic.
If it's not Wi-Fi traffic - i.e., some other form of networking that happens to use a 2.4 GHz radio, but that doesn't conform to any of the PHYs from the IEEE 802.11 standard - you won't be able to monitor it with a Wi-Fi adapter, because it's not Wi-Fi.