8.4's final release was 5 years ago, so unlikely anyone would know the answer to your question.
The only way to really know is to try it.
I just had an issue with the current version (4.11) against PG11.4, where the version of psycopg2 was out of date by a release (2.7x instead of 2.8). Most stuff works, but there are a few things that don't.
Based on that example, I reckon any reply either way is pure guesswork.
We cant upgrade because of business reasons but that is very high on our agenda to fix. To me, there is a huge difference between unsupported and wont work. I dont expect support for this but are there significant changes between 8.4 and 9.2 that would prevent pgadmin4 from working?