Yes, I was referring the the sense that had just been proposed.
I think "suf" is safest here.

I think I misunderstood Jim's question "Is it really an adverb?".
You were asking about the second sense, right?
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In Japanese the PoS of a compound XY is determined by Y.
Thus every suffix -Y really has a PoS, which is the same as the PoS of XY.
Our way of handling this is not perfect.
If XY is a verb, then we tag -Y as [aux-v].
If XY is a an i-adjective, then we tag -Y as [aux-adj].
But if XY is a noun or adverb or something else, then I think we simply tag -Y as as [suf].

gg5 has 事なく済む　
ngrams show 事無く終わっ, 事無く続いて, ...

Often followed by a verb
Functions as an adverb
Either an adverb [adv] or an adverbial phrase [exp,adv].

GG5 - has a separate "-ことなく, -ことなしに" entry for this

Is it really an adverb?
There are 21 sentences with this pattern, so I have reindexed them to this entry.

@@ -23 +23 @@
-<pos>&adv;</pos>
+<pos>&suf;</pos>
@@ -25 +25,2 @@
-<gloss>(after verb) without ...</gloss>
+<s_inf>after verb</s_inf>
+<gloss>without ...</gloss>

https://eow.alc.co.jp/search?q=ことなく

"真はまっすぐ、家にはもどらない。いつも帰り際にゲームセンターに寄るのが日課になっている。そこでは、いつも槙一と一緒だ。槙一がゲームをしているのを見ていると、真は不思議と飽きることなく、時間を潰す事ができた。"

@@ -21,0 +22,5 @@
+<sense>
+<pos>&adv;</pos>
+<misc>&uk;</misc>
+<gloss>(after verb) without ...</gloss>
+</sense>