Multiplying two 32-bit integers will always cost a certain amount of power. Building specialized hardware can get rid of other costs, like the cost of decoding instructions, but the fundamental cost of the multiplications will never go away.
If your algorithm requires a million 32-bit multiplications, that sets a firm lower bound on how costly it is. There is no way to magically perform all those multiplications for free.
Yes and no. Yes, any given multiplier topology will have some fundamental costs, but the lower bound on the energy for any particular set of multiplicands, latency requirements, and precision requirements will often be much lower than building a canonical multiplier. If you can't make assumptions about any of these (e.g., if it's a multiplier in a general-purpose core), the costs are more uniform (though unless leakage dominates, the energy will still be value-dependent, since dynamic energy is proportional to activity factor). In a domain-specific context though, you often can; these assumptions are borne out in the datapath units of nearly any DSP, GPU, or ASIC.
If your algorithm requires a million 32-bit multiplications, that sets a firm lower bound on how costly it is. There is no way to magically perform all those multiplications for free.