Yes, they enter the portal in their final year of undergrad, which allows them to talk to other coaches while still competing at their original undergrad school.
The typical pattern I see in Track and Field: athlete discusses post-grad future with current coach; if that future might be at a different school then athlete registers for portal as grad transfer; athlete/coach contact other schools/coaches; funding offers are made contingent on admission; athlete applies to grad program at selected school or mix of schools.
I have seen cases where admission is immediate because it’s rolling, or denied at one grad program but admitted at another less competitive program at the same school. Almost every school has grad programs that the coaches know will be an easy admit to be used as a sort of safety program.
Of course, there are some athletes who plan grad school separately and then contact coaches when they’re admitted and decide where they want to go.