* In the games, Blaze doesn't remember Sonic. They first meet in *Sonic Rush* and *Sonic Rush Adventure*, but due to the time-space distortion caused by the Sol Emeralds, Blaze forgets their encounter after returning to her own dimension.
* In the comics, Blaze does remember Sonic. The IDW Sonic comics, which are canon to the games, depict Blaze as having a distinct memory of their adventures.
So, it depends on which continuity you're talking about.
The official answer: In the main Sonic game canon, no, Blaze doesn't remember Sonic.
But, in the comics, she does!