It's hard to know definitively, but Champions Tour player Paul Goydos might be unique in that he maintains a handicap index and actually posts his scores from tour events.
For instance, Goydos had scores of 72, 65 and 68 at the 3M Championship over the weekend (he tied for seventh). A check of his handicap index at GHIN.com shows he posted scores of 71, 65 and 68 (we can't explain the discrepancy between his first-round score and his posted score) on a course with a rating of 73.3 and a slope of 146. From the blue tees at the TPC Twin Cities at which the 3M Championship was played, the course has a 73.3 rating and a 146 slope.
There was an additional score of 67 posted from what obviously is the same course. Presumably that was his pro-am score.
In June, he posted this series of scores: 71, 74, 72 and 67. Those were his U.S. Senior Open scores at Del Paso Country Club (he tied for 38th).
Goydos, whose current index is +4.9, maintains his index because when he is home in Southern California he frequently plays matches with his friends.
There is a club, Whisper Rock in Scottsdale, Ariz., that has several tour players as members, and the staff there records their tour scores (Phil Mickelson is a +5.8, Paul Casey a +6.0).
But Goydos posting his own scores from tour events, as well as his scores playing with friends at home, is exceedingly rare, if not unique.