Edge devices don't have Bluetooth audio support, so no. I'm not aware of any other bike computers that do.
You could try with some of the x45/fenix 6 watches that do have music support, although I never tried this with the Varia myself. When paired with a watch, you will get a vibration alert.
But I would have thought that wearing earpods in a situation where you need to use a Varia is a bad idea. (Personally, I use earpods when training at the velodrome, but definitely NOT on the road).
Also note that the alert tones can be customized on Garmin Edge's to be more or less distinctive. gplama has a video on this https://www.youtube.com/watch?v=SaHd6PohRro
You could try with some of the x45/fenix 6 watches that do have music support, although I never tried this with the Varia myself. When paired with a watch, you will get a vibration alert.
But I would have thought that wearing earpods in a situation where you need to use a Varia is a bad idea. (Personally, I use earpods when training at the velodrome, but definitely NOT on the road).
Also note that the alert tones can be customized on Garmin Edge's to be more or less distinctive. gplama has a video on this https://www.youtube.com/watch?v=SaHd6PohRro