It doesn't appear correct to say that the Lord, our High Priest, was tempted like we are tempted. There was nothing Satan could grab, since He was and is sinless. And, having utterly defeated Satan, sin, and death, and coming again to finish them off--and they know it, I hardly think they are a problem for Him, if they ever were, which I don't think they were.
As for us, no, this life is the period of testing and temptation, wherein we make our choice. The saints are no longer bothered by demons, but rather cause them problems. See what St. John, the Apostle of Love, does to them in the live of St. Andrew the Fool for Christ (Oct. 2).