Is there a way to add the Merlin Bird ID App, by the Cornell Lab of Ornithology to the IQ Store? Or is that too much to ask, I'm looking for a way to take my birds on the go without my phone?

No, it’s not possible. What can be done in IQ is limited.

It seems likely the Merlin app needs a fairly fast computer and a fair amount of RAM.

The computers in the Garmin devices are very slow and don’t have much RAM (IQ programs have to be very small).

The Merlin app also needs a microphone (probably, a fairly high-quality one).

If it was possible, the app would also need to be completely rewritten to work on the Garmins. This would, almost certainly, be too expensive to do.