No, the paper targets "constant time" operations, not timing agnostic.

The paper even mentions that blinding works, and that to me is the canonical "separate the time and power use of the operation from the key material" solution. The complaint about this approach in the paper being is that it would be specific to these prefetchers, but it seems this type of prefetcher is increasingly prevalent across multiple cpus and architectures so it seems unlikely to be apple specific for long. The paper even mentions new intel processors have these prefetchers and so necessarily provide functionality to disable them there too. This is all before we get to the numerous prior articles showing that key extraction via side channels is already possible with these constant time algorithms (a la last months(I think?) "get the secrets from the power led" paper). The solution is to use either specialized hardware (as done for AES) or timing agnostic code.

Trying to create side channel free code by clever construction based on assumptions about power and performance of all hardware based on a simple model of how CPUs behave is going to just change the side channels, not remove them. If it's a real attack vector that you are really concerned about you should probably just do best effort and monitor for repeated key reuse or the like, and then start blinding at some threshold.