If you’re working on a Mac, yes you can export a video that has a transparent background. The "trick" is to export as "Apple ProRes 4444". This can then be imported into apps such as iMovie or FinalCut Pro for compositing with other videos. Adobe's Premiere probably works too.
If you’re working on Windows, you have an alternative approach, apart from greenscreen removal, though this will depend on your video editing software supporting this workflow. Here, you have to export a series of PNG files and your video editing software has to be able to import these to reconstitute your CA4 animation. (Note JPG's are no use, since they doesn't support transparency and GIF's have a limited colour pallette. It has to be PNG to get the transparency option.)
If you've used any assets in your animation that you want excluded in your final render, go into the Scene Manager and hide anything you want hidden before you do the final render/export.
I think my double-screenshot highlights the important render settings for both platforms.
76% of original size (was 661x19) - Click to enlarge
Edited 2020-05-24: have checked and confirmed that iMovie works too.
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Cartoon Animator 4 Pipeline (always the current production version, unless otherwise stated)
Mac mini M1, macOS Big Sur (11.6.5)
Signature data last updated 2022-05-15