Do you mean the actual heating load in each space, or the circulation-loop
net load and/or boiler load?

Particularly when ignoring loop thermal losses, putting a VSD on the pump
reduces the pump heat that goes into the loop, which would otherwise reduce
the net loop load and boiler load. So, by saving pump energy, boiler energy
increases. If the boiler is electric, it could be difficult to justify the
VSD, as you would simply be trading electric consumption at one point for
consumption at another.