Can I record audio by connecting my keyboard via MIDI?

MIDI represents a control signal that transmits messages like "Note On", "Note Off", "Pitch" or "Velocity" (and so on), but it does not transmit the actual sound by itself. You can think of MIDI as a set of commands that are controlling a synthesizer (hardware or software), sound moule, drum computer, etc. remotely via a MIDI cable. A device that interprets the MIDI commands is always required. In case of software synthesizers controlled by a MIDI keyboard, your computer together with the software becomes this device.

Because of this, audio and MIDI needs to be connected and recorded separatly. For example, if you use a synthesizer keyboard that has MIDI, you would typically not only connect the MIDI ports to your MIDI interface, but also the audio output of it to your audio interface. To record the audio signal in your DAW software, you need to create an audio track (typically stereo) and record it there. To record the MIDI control data, you would record it to a MIDI track in your sequencing DAW software. Of course you can play your MIDI track(s) and simultaneously record the audio signal (which equals the conversion of MIDI to audio).

The MIDI interface and audio interface you are using can be totally different devices, although many ESI products both contain audio and MIDI interfaces integrated into one product.