Yes, most grids still rely on non renewable resources. But that is simply a relic of the fact that they were built that way. The existing examples prove it's possible.
>We estimate that GHG emissions from reservoir water surfaces account for 0.8 (0.5–1.2) Pg CO2 equivalents per year, with the majority of this forcing due to CH4.
https://academic.oup.com/bioscience/article/66/11/949/275427...
That's between 2% and 3% of our global greenhouse gas emissions. About three quarters of greenhouse gas emissions come from energy production and about 15% of all energy production is hydro power if I recall correctly.
It's much better than fossil fuels, but not quite clean.
There are no countries running on wind/solar, which is the only renewable technology that can actually run everywhere.
Certainly the examples I have given are those that have the easiest path to renewables. It is entirely logical that they would be the first to transition. But it proves that it's possible.