My first greyhound had heart disease, and like the others have said, did not need anesthesia for her echocardiogram. Maybe since Daisy is a spook, just a little Xanax or something like that to calm her would be enough. If not, I would agree with saying no. Sugar started on lasix and enalipril, then moved on to vetmedin as she got worse. All of this lasted about 3 years, then I lost her to kidney failure.
The grain free food/heart disease issue is fairly new over here. Some tests have shown a possible link, and since most dogs don’t really need grain free it seems sensible not to go there.