According to PLC, 俄 can be an adverb and it means "very soon, presently, suddenly". Does this meaning still occur in modern Chinese?
As of all the information I can find on the web, 俄 is used as an adverb only in classical Chinese.
In modern Chinese, this character almost always behave as an abbreviation of 俄罗斯 (Russia), as you can see in the title of some Chinese news saying something like
中俄 (China and Russia) or
俄军 (Russian army).
Some example in classical Chinese:
Very soon, hundreds of people are yelling (for help).
Suddenly, the snow falls heavily.
I have a different answer: yes, we still use it sometimes.
In my 《新华字典》, a dictionary that is only for modern Chinese learners, the explanation of 俄 still includes "短时间".
俄 é 短时间。[俄而][俄顷]一会儿，不久。
In some literature works, the writer still like to use "俄而" or "俄顷" because they sound more beautiful. Yes, beautiful. It is not popular in daily conversation between common people, it is a 书面语. The use of uncommon 书面语 in literary works can sometimes make the article more elegant and graceful. Also, the readers may think the writer better.