All valid questions!
Initially, I liked your thinking, but after a quick thought, here is my counter...
Who fills out an application?
The Application? Gremlins? Or a Person/Customer?
This is sort of similar to the debate with an E-commerce site...
What constitutes a "Customer"?
Is it anyone who visits the website?
Or just people who create an Account and buy something?
In the physical world, most Store Owners see everyone as a "Customer" from the person walking by your store, to someone "window shopping", to someone just browsing in the isles, to someone who bought something.
Of course you have to take a slightly different approach online, but you see what I am saying?
I agree with Jeff in that "Person", "Benefit" and "Application" would be Entities/Classes as far as the implementation goes.
The following is going way farther than I intended, but since we are getting all technical here, this is how I see the larger Requirements to Design possibly going...
Actor Use-Case Objects
------ --------- --------
Applicant Apply for Benefits Person
Recipient Use Benefits Person
I think that is consistent with Jeff's point about "Person", "Application" and "Benefits".
But back to my OP, I think "Customer" vs. "Applicant"/"Recipient" for my Use-Cases is just splitting hairs...