Alternates are typically ranked, so usually the ones at the top of the list will show up. At one point in the past, I think the USGA restricted access to the course by the alternates during practice rounds, but that limitation has since been adjusted due to uproar by the players/alternates. (thanks tigerswood, couldn't remember the exact date that policy changed).
I mean, John Daly got into the PGA as a 9th alternate back in the day, so you'd think anyone who has a shot to possibly get in the field will at least show up on site if they have the means....