When installed as part of Hitfilm 2017, can it also be used with Premiere Pro or After Effects?
No. Adobe software uses a proprietary format for plug ins, while Hitfilm uses OpenFx.
BCC 3D Objects for After Effects can be purchased here. $299.
Thanks @Triem23 one more reason to find Adobe's products annoying lol
Even disregarding the plug-in difference, most/all times a bundled plug-in only works with the host program that bundled the plug-in in the first place. For example, Vegas uses OpenFX but the Hitfilm BCC 3D objects does not show up in Vegas.
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