If she is just a gestational carrier, the answer is no, she isn't. In gestational surrogacy arrangements, the egg cell is provided by the intended mother as long as possible, or by an egg donor if needed. The goal is to avoid that there's a genetic link between the GC and the baby-to-be in order to prevent the creation of an emotional bond between them.
Conversely, in traditional surrogacy, the surrogate is the biological and birth mother at the same time. This is precisely the reason why this kind of surrogacy is not practically not used today in the USA.