It will get stuck at liquidity preference. In other words, no, interest rates won't be determined by available savings, in fact the opposite will happen. People will actively withdraw money from the economy to extort interest beyond what the economy can pay.
Companies will pile up inventories until they realize that they should stop producing and fire their workers and instead just hold this perpetual motion machine money instead of running a productive business. Yields from speculation trump yields from production, see cryptocurrencies.
Then as more and more businesses quit, prices will rise and you get to see inflation. The speculative bubble will collapse and the cycle repeats, just like with cryptocurrencies, except you will lose your job and your income will fall.
In short, the interest rate will get stuck at some above market clearing rate.
If we assume the presence of Oeconomia Augustana banks next to the regular banks and that people will quickly switch to this type of banking, then the absence or presence of central banks or whatever policies they make will be utterly irrelevant because under OA banking, the interest rate is actually market oriented.