They can. It can also greatly reduce wear and tear on the hardware. But it's not a bolt-on job doing it.
There are many, MANY details that need to be understood and handled to do the implementation. It would need to be backed by a PLC with temperatures, High-side and Low-side pressures, watching everything and providing adjustability and control. You'd also want to VFD the condenser fan(s).
This is what I'd call a graduate project, not for anyone with only a basic understanding of the details of refrigeration. Without the chops to do it you will maybe save a little energy but no where near enough to replace the failed compressors and deal with the resulting accidental system burn-outs.
You used the term refrigeration, so I will work with the assumption that you actually mean refrigeration.
With that assumption - all other things being equal - no, there is not much opportunity for energy savings. Because the energy needed is directly proportional to the heat transfer into the refrigerated space as a primary determinant.
The same factors that drive heat transfer also off course affect the performance of the refrigeration system in other ways, some of them non-linear, Some of those factors in theory could provide some opportunities for energy saving via VFD - all other things being equal (and unstated).
But, in refrigeration all other things are never equal.
The performance of each component affects the performance of all the other components. Because, system.
It is never ok to focus on the performance of a single component when looking at refrigeration.
We might assume that conditions exterior to the refrigerated space and the condensing unit are the same.
What are the design conditions? Where are they relative to peak efficiency of the refrigeration system?
If we assume that the system is designed to operate near peak efficiency at design conditions then there is almost no opportunity to improve efficiency.
As the exterior temperature increases the system system needs to work harder, possibly falling off peak efficiency. In that case there is the theoretical opportunity to gain back some efficiency by trading instantaneous work for duration.
Except that if the system is reasonably sized for capacity this will cause insufficient capacity, and the refrigerated space will get warmer.
System.
Also, depending on the type of lubrication system, the allowable window of speed can be very small. Go outside that window and the compressor dies from insufficient lubrication.
As Itsmoked correctly implied, this is non-trivial.
