Legal Question in Civil Litigation in California

Of course. Not every out of state corporation must register; there are many exceptions. Furthermore, even if illegally not registered, that does not prohibit an attorney from representing it nor prevent the corporation from having counsel. It just means the California resident can file a motion to have the case thrown out, or the corporation's pleadings struck from the record unless and until the corporation registers as required by law..

As long as the litigation is in California, then sure.