The answer to this question is yes.  In fact, this is commonly done for planning purposes - the person creates a "pour over will" that leaves everything to a trust.  He or she then creates a living, revocable trust at the same time and appoints himself/herself as the first trustee.  The trust also names one or more successor trustees and provides for distribution of the Trustor's assets after death.  This "avoids probate" and allows distribution of assets without court involvement.