No, 赫斯 wouldn't be pronounced anything like "Hess", and nobody would intuit it as a kanji representation of Hess unless that person were very, very familiar with Chinese renderings of western names.
Using Japanese skillfully means knowing when to use kanji, hiragana, and katakana. Trying to force western words or names into kanji in the belief that the kanji makes them more "authentic" is a mistaken understanding of Japanese. Better to use ヘス, as that is the most proper and easiest to understand rendering of the name.
Also better to use エレベーター than 昇降機, and better to use アメリカ rather than 亜米利加, etc... Katakana is 100% Japanese, so rendering foreign names in katakana is correct, legitimate, and much more appreciated by the reader.
I leave you with an image from well before the war showing that the Japanese were already transliterating western names into katana rather than trying to find kanji that approximated the sounds of the name.
View attachment 31972