Dictionary form: お礼{れい}をする
Transformed into ず-form: お礼をせず
Is お礼をせず used similar to the English expression "without thanking" which itself can work as an adverb, e.g. I ate without thanking
わたしはお礼をせず食{た}べた。
Dictionary form: お礼{れい}をする
Transformed into ず-form: お礼をせず
Is お礼をせず used similar to the English expression "without thanking" which itself can work as an adverb, e.g. I ate without thanking
わたしはお礼をせず食{た}べた。
Yes.
However, something to be careful of is 〜ず vs. 〜ずに:
お役に立てず、申し訳ありません。
"We apologize for being unable to serve you."✗お役に立てずに、申し訳ありません。
お礼も言わず(に)食べた。
"He ate without saying his thanks."
I think you could say that 〜ず allows for exactly what なくて supports plus adverbial modification, while 〜ずに only allows for adverbial modification.
Strictly speaking the answer is no.
Just the -ず ending by itself won't create anything "adverb-like". That's why it takes the "ni" particle (-ずに), to become adverb-like (just like 自由 jiyuu is freedom and 自由に jiyuu ni is freely).
When you have a -ず ending you have a 連用形 ren'youkei, also known as ます形. It follows a negative base (未然形 mizenkei), but the auxiliary verb isn't negative, it's, as I said, a ren'youkei, meaning that it's more like a substantive than an adverb.
When it takes "ni", it becomes "adverb-like", usually depicting the way something is done. In this case it compares to a ないで ending.
Without "ni" it's like a なくて ending, meaning the sentence will be something like "[subject] don't A, and [subject] do B".
It's pretty straightforward if you think about it. You can coordinate two sentences with a て形 te-kei or with a 連用形 ren'youkei (in different contexts). But what if you want to coordinate a negative sentence? The first one becomes nakute, but the second one? You can use ず (、), because, yeah, it follows a negative base (未然形 mizenkei), but it's a ren'youkei if it comes to the auxiliary verb -ず.