Does Peter say Joel's prophecy was fulfilled at Pentecost?

Yes, and his exact words leave no room for ambiguity. Acts 2:16:

"This IS that which was spoken through the prophet Joel." — Acts 2:16

The Greek verb estin is the equative "to be" — not "this is like what Joel said," not "this resembles Joel," but "this is that." Direct identity. Peter uses the same logic Jesus uses in Luke 4:21 when he reads Isaiah 61 in the synagogue and says, "Today this Scripture has been fulfilled in your hearing."

But what Peter does to the text of Joel is even more revealing. Joel 2:28 (LXX Joel 3:1) says the outpouring will happen "after these things" — an indefinite future. When Peter quotes it in Acts 2:17, he changes that phrase to "in the last days." He's not misremembering. He's interpreting: what Joel called "after these things" is what Peter is calling "the last days" — and they have arrived. Peter also adds "says God," which isn't in Joel at all, underlining that he's making a theological declaration, not just reciting a text.

The word that starts Peter's sentence matters too. Acts 2:15 ends with "it is only nine in the morning," and then verse 16 opens with alla — "but." That's a strong Greek adversative. Peter isn't saying "here's another explanation for what you're seeing." He's saying "the drunk theory is wrong — this is prophecy being fulfilled." He reaches for Joel because Joel is what's happening.

If the church age were a historical parenthesis that the prophets never saw coming, it would be strange for Peter to explain Pentecost by quoting a prophet. He quotes Joel precisely because Pentecost fulfills Joel.

For the full grammatical analysis, see the study on dispensationalism, section "Peter at Pentecost: 'This IS That.'"