Short Answer: it is used in a way that the phrase guy ideal is used in this same passage: here, guy ideal is Holly-speak for ideal guy. DamkerngT has given an apt idiom: Mr. Right. So, yes, it means what you think: "something that is perfect or complete," although since we are talking about a person, it might be better to say "someone that is perfect or complete." The text is quoting Holly Golightly, the main character of the novella.
Longer Answer: In this passage, and the sentence previous to it, Holly is explaining why José is not her "ideal guy" or why "he’s not [her] idea of the absolute finito." The sentence just previous to the text you have quoted says:
Actually, except for Doc, if you want to count Doc, José is my first non-rat romance.
So, Holly begins by saying something positive about José (saying that he is not a 'rat', an expression Holly uses throughout BAT to describe guys that are jerks or worse), but then qualifies that by saying he is not her idea of Mr Right, ideal guy, or absolute finito.
Absolute is an intensifier, which can be used with both 'positive' and 'negative' descriptions: He's an absolute dream. He's an absolute jerk.
Finito can have a neutral, positive, or negative meaning in Italian, just as finished can in English. In Italian prodotto finito can mean '"finished product" or "end product" (although I did not know that until now).
"Finito" does mean "finished" in Italian, and it means nothing more than "ended" or "over" or "done". My answer is almost finished. But in both English and apparently Italian, the word can have a negative meaning (see WordReference). As I said earlier it can have a neutral meaning: finished or end product (Source: WordReference and my app Italian-English Dictionary). Holly is using it in a positive manner. Holly doesn't speak Italian (in BAT, her agent has given her French lessons), so it's a phrase she has either picked up from someone else or made up herself (like quel rat--literally What a rat!). Also, per Wiktionary finito is also a cognate word in Spanish and Portuguese, from Latin.
Henry, you did a great job of including a lot of context with this question. That's very important, especially when looking at a phrase that is not a standard phrase in English.
By the way, I've read Breakfast at Tiffany's (BAT or B@T) more than any other thing in print except parts of the Bible. I have read BAT probably 15 times, and half of those have been "close readings," paying close attention to every word and phrase to try to discover what author Truman Capote is actually saying, as opposed to what readers might read into the text.