Double negation is valid grammar in the Greek. For example (Luke 4:2):
οὐκ ἔφαγεν οὐδὲν / He ate nothing
Lit. "Not [did] he eat nothing"
So this would not in itself be an indicator that the phrase is a question.
If John 16:24a were a question rather than a statement, it would fall under one of four types1:
Is he the Christ? / ἑστιν ὁ Χριστοσς;
(You are probably aware that in Greek ";" takes the place of "?")
Use the word μη or μητι:
Is he [perhaps] the Christ? / μη (or μητι) ἑστιν ὁ Χριστοσς;
Questions expecting the answer "No"
Same construction as hesitant questions, but different interpretation:
He is not the Christ(, is he?) / μη (or μητι) ἑστιν ὁ Χριστοσς;
Questions expecting the answer "Yes"
Use the word οὐκ or οὐχι (contraction of οὐκ- and -τι):
He is the Christ(, isn't he?) / οὐκ ἑστιν ὁ Χριστοσς;
The suggestion you are making, I think, is along the lines of a question expecting a "yes" answer: "You asked for things before in my name, haven't you?" But this can't be a literal interpretation, because there is no οὐκ or οὐχι in the verse.
One could try to argue the case that Jesus was simply asking a direct ordinary question, but this doesn't seem to fit in with the negations in the verse.
Furthermore, it doesn't seem that the Greek Church Fathers in antiquity read this verse this way (i.e. as a question). John Chrysostom, a 4th century Byzantine Greek, for example, makes the point that 16:24 is part of an overall discourse wherein Jesus is comforting the Apostles because he just told them He will be leaving them. As a consolation of sorts, they will see that in the future they will receive a new gift - of His granting them what they ask in His name, even though they never asked anything of Him previously:
Hence He showeth it to be good that He should depart, if hitherto they had asked nothing, and if then they should receive all things whatsoever they should ask. “For do not suppose, because I shall no longer be with you, that ye are deserted; My Name shall give you greater boldness.”2
This is further explained by later Greek commentator, Theophylact of Ohrid (1055-1107):
"Until now," He says, "have ye asked nothing in My name; from now on, ask, and ye shall certainly receive. Thus another benefit from My death is that henceforth you will have greater boldness with the Father. Do not think that because I am physically separated from you, I have abandoned you.3
1. For a discussion of this, see Wenham, The Elements of New Testament Greek (Cambridge, 1991), p.75
2. Homily LXXIX on John (tr. from the Greek)
3. Explanation of the Holy Gospel According to St. John (tr. from the Greek; Chrysostom Press, 2007), p.241