He could have been Lord Protector instead of Cromwell IF he had wanted the job but he didn't. I doubt that he would have accepted the post even if Cromwell was out of the picture. He seemed to be thoroughly disillusioned with Parliament by the end. You need to change his personality to get him to even consider it.
However given that he does take the reins it is who follows him that will decide if the Commonwealth survives. The OTL bunch didn't seem to be able to make a go of it or Charles wouldn't have been asked back. There didn't seem anyone capable of being the equivalent of Adams or Jefferson.