No, it's usually (or almost always) a noun. 後世に isn't adverbial; it's used in expressions like 後世に伝える, 後世に残す, etc. I think 後世 can only be an adverb at the the start of a sentence or clause (with the meaning "in the ages to come").

More that it's a noun mostly used adverbally.

I think its  primarily a noun and our glosses are noun glosses.

@@ -14,0 +15 @@
+<pos>&n;</pos>
@@ -16 +16,0 @@
-<pos>&n;</pos>

後世が	1814

I think it's primarily an adverb.

I think "life to come" usually refers to a supernatural afterlife

Is [adv] right? It's often used with the に particle but this isn't what I'd consider an adverb. The GG5 examples make it seem like a normal noun.

Google N-gram Corpus Counts
╭─ーーーーーーー─┬─────────╮
│ 後世　　　　　 │ 511,542 │
│ 後世に　　　　 │ 304,798 │
│ 後世の　　　　 │ 106,297 │
╰─ーーーーーーー─┴─────────╯

@@ -17,0 +18 @@
+<gloss>future generations</gloss>
@@ -19 +19,0 @@
-<gloss>life to come</gloss>