Yes, Busylight is compatible with Skype for Business, but not the free version of Skype (for consumers). Skype is, however, approaching its end of life soon and Microsoft intends to replace it with Teams as their default communications platform.
Please note: Busylight won't start if there no compatible Microsoft Lync or Skype4B client installed. Skype for Business 2016 – One common error If Busylight does not start or function correctly after Office was installed or updated (and some cases removed), it’s typically because some registry values got messed up - in particular when upgrading to
You still need to have Skype for Business installed on your PC in order for the Office API to apply itself to the remaining Office applications.