No, it doesn't. Different algorithms can vary pretty wildly in performance based on the design of the hardware they run on. For instance cache sizes can make one implementation of a sort on a certain sized dataset faster or slower than another. You can have a theoretically fast algorithm that just isn't as cache efficient as a theoretically slower one in big-O terms. All levels of the memory hierarchy as well as storage have specific bandwidths and latencies that inform the real world performance results. Parallelism is another issue. Many cores can do work very fast when you're careful about how you split up work between them, taking into consideration the synchronization latency and individual cache sizes and so on. The best approach for doing work on 64 cores can be dramatically different from what works best on 1 or even 2.

That is not a given. A database server can run faster on better hardware because it more effectively and aggressively caches things in memory, which can hurt it on lower-spec systems. Or it can better utilize SIMD instructions that are not present on the low end. Or it is more effective at utilizing more threads, but is slower when run at a low threadcount, etc etc etc.

If I'm not mistaken ClickHouse's min spec is quite steep.