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Yes that is pretty much what it means, although leveled out horses do still gain very slowly (a small fraction of a point per training). Leveled out horses can be the best show horses in your herd if they have a decent score for their show level.

It sounds like she has a VERY low PT score--not a show horse at all. Horses like this can make good breeding stock, but they are among the few who will not pay to show. I would guess that her PT score, if you tested her, would be no more than 3 and is more likely to be less than one. (0.5, for instance.) Without a doubt, Dorris would faint when you brought her in for testing. *G*

So, you can continue training her, if you'd like, since it doesn't cost anything but the time to do it, or you can just let her sit and see how she turns out as a dam.

Her base score was probably right on the edge between grades in level 1. That would be why she leveled up with the second training. If you give us her link, we could check her out for you.

As an exceptional producer she definitely be a good breeder, even though she will be useless as a show horse. With foundations there is absolutely no connection between breeding and training ability. When you push the Create a Horse button, the game generates 2 unconnected random numbers for the breeding and training scores. With lined horses the breeding scores of the parents are combined according to a secret formula which includes a random factor once for the foal's breeding ability and a separate time for it's training ability. There is some connection since the parents breeding abilities are used to generate both, but the random factor means there is considerable room for variation.