Yes, you can run individual channel outs from the insert points. If you plug in a 1/4 plug just to the first indent, not all the way in, that will send whatever signal is present at the channel in, out to your interface.
If your mixer has bus channnels, you can also send out from them to your interface. This is probably the most common method used because it allows you to use the channel gain, EQ, and FX returns prior to going to hard drive.