Nope, you don't collect half of something and hand that in then go get the rest at another date.
Realistically you'd go with a complete collection otherwise someone would come after you've entered some then they;d finish it off and get the prize.
That's true, but it's not like you have any competition for the prize.
More to the point: nothing Festus says indicates that you have to hand all 50 in at once, which makes it seem odd when he doesn't accept them until you have 50. Yeah, from the POV of the promoter it would be silly to allow it, but it would be a reasonable game-play concession since the Courier is the only one who can actually turn them in.
I see why they didn't add it in, though, since the whole point of the exercise is to encourage the player to thoroughly explore the Mojave to find the things.