It doesn't seem that way.
Most efforts to legalise abortion are based on the argument 1) that women have a right to do what they want with their own body, or 2) that abortion has social benefits. And since the progressive side of politics is making no real effort to stop abortion after the embryo has become a foetus and developed a nervous system it's probably safe to assume that women's rights and social benefits are far more important to them than whether an foetus is 'sentient being capable of experiencing'.