Is there a way to test a design time component without recompiling the IDE each time a change is made?
For the design time features you must recompile the IDE. It can be sped up by having a minimal set of packages. Only the packages needed by the IDE itself + your own package.
The "BigIde" target used for release builds contains many extra packages.
Your component's functionality however can be tested by creating the comp in code and then testing + debugging. That is typically the biggest part of development.