There may be some savings in term of power, but it will strongly depend on the nature of the compressor operating curve (corrected curve at the given operating speed). Normally throttling outside compressor (i.e. at suction) will cause some PD at the inlet valve and thus reduce the compressor discharge power. The compressor will still pump the required volume, but the operating region will change, this can help in some power savings. However, it is a strong function of the operating efficiency and in case the new region falls in bad efficiency region, the savings can be upset by this loss.
There are some other options also worth considering here. The compressor vendor can be contacted for looking into the possibility of providing inlet guide vanes / or similar device. This is a better option as the vendor will be aware of the nature of curve and can design a optimized guide vane / louver type of device. The second option is to look into impeller trimming. This option is very well proved for centrifugal pumps, but will have to be looked cautiously for compressors (as the compressor stability, leak / bypass, efficiency can be greatly affected). Here also the vendor can give his advice for feasibility of the option.
Finally, some advantage can be gained if some type of speed variation is possible in the compressor. In case it motor driven; a VSD can be considered. In case of steam / gas driven feasibility of using a governer to reduce the operating speed can be looked into. This option will reduce the compressor efficiency, but will give the best power savings (if feasible) without doing a lot of change irreversible changes in the system.