To accurately answer this question one needs to know its context: does "self-reflective" refer to the author, Samuel Beckett?
If the answer is afirmative, then yes, there are many aspects in the play which could be deemed to have been an attempt by the author to reflect on his own situation and his understanding of his place in the greater scheme of things, or rather, his opinion thereof. Also, is this self-reflection deliberate? Yes. The play clearly indicates the deliberate manipulation of an ordinarily mundane and insignificant event, "waiting," into something more than it actually is. Beckett deliberately forces the audience to attempt the insightful appraisal of the events being depicted, just as much as the play could have been, for him, the deliberate confrontation of a universal conundrum: the purpose of our existence.
However, Beckett, just as his play does, made it fundamentally difficult for others to understand his writing or its purpose. When asked why he had written the play, he said that he had done so
"as a relaxation, to get away from the awful prose I was writing at the time."
This suggests that Beckett deemed writing the play a form of escapism. It is relevant though that this escapism saw him focusing on a fundamental philosophical question. He furthermore scoffed at others' opinions and interpretations of his work, so much so that when asked by actors to define and explain the characters in the play, he merely shrugged his shoulders. He further wrote:
"Why people have to complicate a thing so simple I can't make out."
It is patently clear that Beckett was deliberately evasive about the meaning of his play. This further deepened the mystery of his purpose and ties in with Beckett's controversial views with regard to language. He believed that language could not be used to define inner consciousness and that it was an intrinsic part of the human situation and could thus not exist or function as a removable element.
The play therefore brilliantly depicts this perspective. The fact that we cannot understand exactly who or what Godot really is adds to our confusion. The characters use words as opposites and as synonyms, derive meaning from the meaningless, use florid language, make lewd suggestions, references to biblical text and indulge in meaningless and flamboyant diatribe. This perfectly conveys Beckett's idea of how language is meaningless since it cannot truly express what is real - the core of what we truly experience.
Samuel Beckett has illustrated through this play that language is a wholly inadequate vehicle for expressing fundamental truths, and as such, we cannot definitively convey our purpose, our reason for existence.