Disclaimer: Undertale belongs to Toby Fox. This was done for non profit/for fun purposes. Special thanks to Grimmik for footage. Annnnd we have another one. I just love voicing characters where I have to constantly change my vocal range!
You do good Flowey stuff :) Personally, I always figured Chara's name was pronounced "care-uh" as in *chara*-cter, but I guess that's why I don't do dub work :3
Short answer: No. Long answer: It's debate, maybe/kind of on technicalities. Short answer: Flowey mistakes Frisk for Chara almost the entire game. So the standard interpretation of this scene is Flowey is just mistaking for Chara. Long answer: However, there is a LOT of evidence Chara is indeed the narrator of the game (google it, there's hundreds of quotes supporting it and it's a very common fan theory, to the point many consider it canon since it's so well supported). If Chara's personality/memorizes latched onto Frisk, I believe you could put this is the "kind of" category. There's a few other fan theories (like reincarnation or sharing a soul) that also fit this, but those are MUCH less supported. However, at the end of the Pacifist run Asriel does say that he realizes Frisk and Chara are NOT the same person, and despite their similar fashion sense he doesn't know why he mistook one for the other. This would support that he was only mistaking one for the other.