You colud just search the web to find out about Audigy2
Here it is:
It is a plain old (2004.) PCI soundcard. (I have this one in the picture: Creative SoundBlaster Audigy2 Value). Maybe stiil a little bit advanced than onboard HDA cards.

But, the main thing here is that it is supported by ALSA as wavetable (MIDI) device.

Now, I'm at different PC where I have Realtek ALC888
$ aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: Intel [HDA Intel], device 0: ALC888 Analog [ALC888 Analog]
  Subdevices: 0/1
  Subdevice #0: subdevice #0
card 0: Intel [HDA Intel], device 1: ALC888 Digital [ALC888 Digital]
$ cat /proc/asound/card0/codec#0 | grep Codec
Codec: Realtek ALC888
And we can see, no MIDI devices related to it
$ amidi -l
Dir Device    Name
Also, in alsamixer there is no "Synth" fader like for Audigy2. So, if the onboard HDA cards actually have MIDI chip & bank inside them, I really doubt that they are supported by ALSA. I have to admit that I didn't go to find out if one could "activate" MIDI chip & bank, so I really don't know if it can be done or not.

I suggest that you try to go the software way with Qsynth. It has default sf2 which is 140MB, and that kind of bank surely will sound better than any potential bank in onboar chip. Also, with Qsynth you don't need to use JACK for audio. It can play as just ALSA application, although you will need to connect MIDI ports with "aconnect" or similar.