I think it's called a "non-roster invitee". This, from an official press release (email), from the Boston Red Sox:
Hello Boston Red Sox.com subscriber, you are officially invited to Spring Training with the Boston Red Sox! Play in the sun with the team and experience what spring training is really like down in Ft. Myers. For a nominal fee of (Let's call it a half year of mortgage payments) you can be at the games just like the pros.
We hope to see you down in sunny Florida when the Red Sox take the field for the first time in 2010.
See, told you. It's always been a dream of mine to play for the Boston Red Sox, but I thought they were supposed to pay me, not the other way around. I think this engineering gig has kind of run it's course. It's time for something new.
I've taken the liberty of creating my own baseball card. It's a 1987 Topps in case you didn't recognize the sweet wooden border.