You didn't specify a manufacturer, I will assume Cisco switches though most other vendors should behave similarly.
If the channel group's mode is active, the interfaces will not forward traffic, since the switch will actively be trying to form a channel and if the channel negotiation fails, the port channel will be "down".
If the channel group's mode is passive or analog to passive, the interfaces will forward traffic normally and will listen for LACP/PaGP negotiations. This will bring the interfaces up and listen for traffic on the interfaces. If the switch sees these LACP packets from the host and a negotiation commences, the channel will be negotiated and packets will be forwarded over the port channel interface and not the individual interfaces.
From the server's perspective, at the IP layer, if the destination host is in the subnet defined by the network configuration on the interface, the server will attempt to ARP this address. If somehow both interfaces were connected to the same subnet (most OS will show a warning or disallow this behavior), they may ARP out both interfaces. So once the ARP is received on a given interface, the server will know to send the packets out this interface, and the switch will also identify which IP and MAC are tied to each individual interface (but the forwarding behavior will be controlled by the below).
If you are purely talking about Ethernet packets, and not IP, the server will forward the frames using whatever interface is specified. If I am not mistaken, in Linux the interface MUST be specified; in Windows it will probably use the interface with the highest (top) priority in the network interface bindings. This behavior varies OS to OS.
From the switch's perspective, the switch will flood frames with a MAC address out all interfaces until it learns which port a given MAC address is on. It will learn this port by listening for a frame with the source MAC address. So if 0111.2222.3333 is sending a frame to 0111.2222.3334, the switch will flood the frame out all ports in that VLAN
0111.2222.3333 (Fa0/1) -> 0111.2222.3334 will flood to all ports
Until it sees a reply
0111.2222.3334 (Fa0/2) -> 0111.2222.3333 (Fa0/1)
Then it will commence forwarding all traffic to the specific port that issued these frames.
There are a number of edge cases here that might bring more confusion such as the potential spanning tree interaction, but this covers the basics.