Indeed it does. It's just that part where she wonders how she can communicate with Cloud that seriously gives me dream date vibes.
I got a similar read. IIRC - Aerith mentions wanting to tell Cloud things that she was unable to. And wanting to meet him, but only as how he remembers her.
Seeing how Aerith contemplates her "suki," by the end of the dream date, perhaps its after those state of events where Aerith comes to the realization of what Zack actually means to her (in that she always loved him). I am inclined to think its somewhere after COLW!Aerith and before AC!Aerith. These lines from her monologue seem like they could fit in that timeframe.
"This place is a strange place, the seasons never change, my feelings never change" (paraphrase)
"Ugh, that's it! I give up. I can't stop thinking about you." (paraphrase)
Also, COLW mentions Aerith having the ability to dissolve into the LS but she doesn't because she needs to stop Sephiroth. At the end of AC, we see Zack and Aerith walk off into the LS together ("Her first love always at her side" - paraphrase). This indicates to me that Aerith may have found a way to co-exist with Zack in the LS which could be one of the reasons why she chooses not to dissolve in the LS.
Just speculation, could be wrong. Interesting how it kinda lines up though.