I don't know that there's a way to tell if the registry doesn't have the DNA test for the horse you think she is. I have a few friends who've done the AHA DNA tests and gotten back a name because their horse was registered with DNA but others who have gotten nothing back. I have a grade Arab or at least part Arab mare I thought about sending DNA in for but the cost is pretty high so I'm not sure.
Just an FYI, not sure if you care but the AHA is super unhelpful about paper transfer if that's what you're hoping for. I have a DNA tested registered gelding, I know his number and name but his breeders refuse to sign his papers over (he was a halter horse who failed due to a crooked tail and they dumped him at an auction when he was unsuccessful at that and they don't want anyone knowing he's theirs) and the AHA says there's nothing they can do to help me unless they sign them over. A little frustrating and I'm hoping they can change that policy someday. The above mentioned friend who got a match back from her kill pen horse found the registered owner but they as well wont sign over papers so she can't get them either.