Are pure Korean words like 가람 still used in speech or writing instead of Chinese borrowings like 강 ?
Short answer: No.
There used to be popular TV shows that created a trend of re-discovering pure Korean words like in 2000s, and some have become popular since then. However, many others are still obsolete, and 가람 is one among them. It's just that some people know 가람 means rivers, but it is rarely used for daily usages. I wouldn't expect people to understand what I mean when I say 가람.
I've seen 가람 being used for names for people or businesses though.
I think you should consider these old pure Korean words somewhat like jargons. When you say it, people may or may not understand you.