Yes, this works, but probably 50/50 if you get your card signed by an equipment manager.
If you are interested in retired players, there are websites/groups of people who send cards directly to players homes and that seems to be more successful. The addresses are published along with success rates, turnaround times and fees players charge for this. Most are $10-$20 for each card, but this is for Hall of Famers like Ryne Sandburg, Wade Boggs, Andre Dawson, Mike Mussina, etc. Nolan Ryan charges $75 I think. They may have addresses of current players as well, but they’ll be heading to Spring Training shortly.
I did this back as a kid with marginal success and just stumbled across this again with a suggested group on Facebook a week ago. I have auto requests to Rollie Fingers and Sonny Jurgensen going out tomorrow, so we’ll see how that goes.
Search TTM (through the mail) Autographs and you’ll get all the info you need.