Does the term "graduate applicant" mean "a person who applies to get graduated" or "a graduate who applies for something"? If it is the second one, what can we call a person who applies for a graduation program?
As Kosmonaut said, the phrase is probably ambiguous as it stands, though the context will probably determine which is meant. To avoid confusion, I would suggest using the following:
Someone who is in the process of graduating is known as a "graduand". That's what you are referred to as on your graduation day.
Someone applying to a graduate programme could be a "graduate school applicant"
And perhaps "graduate job applicant" to refer to a graduate, applying for something else...
My initial assumption on hearing the phrase was equivalent "graduate school applicant."
I would call someone currently matriculated who is applying for their degree a "bachelor's degree candidate" or "PhD candidate," etc.
I would find it confusing as "a graduate who applies for something" unless it was in a very specific context. What did this applicant graduate from? With what degree? It's too vague to be useful unless the context provides more information.
But this is admittedly based solely on my own usage (Northeastern United States).