Short answer. Yes. From the filing of the petition the spouses are entitled to live separately from each other. You do not need the court's permission or your spouse's consent, and leaving after filing is not abandonment — the entitlement comes from the Family Code itself.
What the law says
After the filing of the petition for legal separation, the spouses shall be entitled to live separately from each other.
Family Code, Article 61 — Living Apart and Property Administration During the Case. Read the full provision →
What the law says
The court, in the absence of a written agreement between the spouses, shall designate either of them or a third person to administer the absolute community or conjugal partnership property.
Family Code, Article 61 — Living Apart and Property Administration During the Case. Read the full provision →
The right begins on filing
Married people otherwise owe each other the duty to live together, which is why so many petitioners worry that moving out will be used against them. The article removes the difficulty: After the filing of the petition for legal separation, the spouses shall be entitled to live separately from each other. The entitlement attaches on filing, not on the decree, so it is available throughout the six months before the case can be tried and for as long afterwards as the case runs. It belongs to both spouses equally.
Living apart is not the same as leaving the marriage
Separating under this article does not affect the marriage, does not end support obligations, and does not by itself settle who the children live with. Those are decided on their own terms. It also has nothing to do with the abandonment ground, which requires an absence without justifiable cause; exercising a right the statute gives you is justifiable by definition. What it does is make the practical arrangement lawful while the case proceeds.
The property has to be looked after by someone
Two households and one property regime is where the friction usually starts. The article deals with it: in the absence of a written agreement between the spouses, the court shall designate either of them or a third person to administer the absolute community or conjugal partnership property, and the appointee shall have the same powers and duties as those of a guardian under the Rules of Court. That is a fiduciary role — the administrator manages the property for the regime, not for whichever spouse holds the position.
Agree it in writing if you can
The article prefers a written agreement and only appoints an administrator where there is none, so spouses who can settle who manages what will save themselves a contested application. Where agreement is impossible, or where one spouse has been dissipating funds, that is the point to raise the appointment. And if leaving the home raises a question of safety, the protective remedies available in cases of violence in the home are the faster route and are not dependent on this article at all.