Yes, you can use the currently poorly named 'initialValues' compartment for SysML "initial values" in a deep Block context, as opposed to the class-wise UML default values; but I can bet that you barely ever will.
What you will use them for in systems engineering, over and over, is for deep configuration of systems in different configuration or test contexts! It is an extremely useful, indeed critical extension of SysML over UML!
I have been using this feature a lot for some years with real world clients. Nearly all of them find the term 'initialValues' completely, utterly, confusing, especially after just having been introduced to the 'defaultValue' concept.
Case: A construction group uses the initialValues capability to describe multiple "deep" configurations of buildings in different modes and customer configurations. They find the term 'initialValues' completely confusing and misleading.
Case: The mobile phone initialValues sample available for MagicDraw/Cameo is in fact a "deep" configuration example (and an excellent one) and has nothing to do with "initial values".
I also have a course session dedicated to how to use this feature for "deep" configuration of systems. Attendees find the term 'initialValues' completely confusing, I now tell them to simply call it 'contextValues' instead.
And as for time? If you want to use the feature to show the value state of a system at different times: t0, t1, t2, t3 in different block contexts you can't; because the compartment name 'initialValues' makes it sound like every time slice is the initial time t0.
The compartment name 'initialValues' truly has to go. It does not work. The compartment name 'contextValues' works for all cases.
And if you do want to use the capability for initial values, you could simply apply a custom diagram stereotype keyword «initialValues» to your IBD diagram as a special context case.