YES.
An adjudicated 'legal separation' can be in effect for years and years ... until death.
However, there is a difference in the usage of the phrase 'legal separation'.
In CA you can get an adjudicated legal separation which divides property & debts, issues orders on child and spousal support, but does not dissolve the marriage (it allows health insurance to continue between the spouses).
There is also the statusof being legally separated (not adjudicated) which is simply that you are both living apart and neither has filed in court. You may reconcile or you may split forever.
Either way, you're in CA.
CA doesn't care who or what you are sleeping with, never mind dating, as long as there is no inappropriate sexual activity in front of the kids.
... Dating may affect your chance of a reconciliation with your spouse.