Sorry, I said that with the adverb/adjective thing because I wanted to make clear that you cannot say that someone είναι αργά, someone is αργός or αργή and that means slow, not late. In Greek, we use the verb αργώ/καθυστερώ or αργοπορημένος/καθυστερημένος (for the meaning of after the scheduled time). I'm sorry i'm late=Συγγνώμη που άργησα/καθυστέρησα, συγγνώμη που είμαι αργοπορημένος. I'm late for my job!=Έχω αργήσει για τη δουλειά μου. For the meaning of "near the end of the day (as in the sentence above)" we use αργά. It's late, let's go home=είναι αργά, ας πάμε στο σπίτι.
Yes αργά is an adverb. And it does not mean late in the meaning of "after the scheduled time", just near the end of the day. So you cannot say that αυτός είναι αργά it's like saying "he is slowly/he is near the end of the day". What does slowly/near the end of the day has to do with "is"? (adverbs apply to verbs) But είναι αργά means η ώρα είναι αργά=the hour is near the end of the day (and makes perfect sense).