Is it possible and acceptable to transcript foreign names into hiragana instead of katakana for aesthetic or other personal purposes?
How would Japanese people judge this choice? Would they perceive it as a mistake?
Don't do that. You have to use katakana for foreign names in almost all cases (excluding Chinese names where kanji can be used).
The only exception, maybe, is when you want to be a comedian/etc and want to play a childish, cute or simple-minded character under that hiragana name.
The general impression of hiragana ばらく・おばま (instead of バラク・オバマ) is described here. If I see ばらく・おばま, I would think it's a mistake, or it's a kind of ゆるキャラ inspired by the US president with the same name.
Addressing foreigners using hiragana can be insulting in many contexts, too.