Absolutely. Not only can you do this, extraction using a centrifugal extractor is what Abbe Warré preferred / recommended in his book (also discusses gravity draining/straining through a sieve). The suggestion that Warré beekeepers only press comb for honey extraction is a modern manipulation of the historical narrative.
Warré had a minor difference in his methods as the frames did not use wire (and there were also frameless variations of his hive). To avoid the comb breaking up in extraction he placed it in wire cages which were then placed into the extractor. If you are using frames, this can be easily and cost effectively replicated using cake drying racks on the outside of the comb when they are inserted in the extractor cages. If you are using the Australian/Modified Warre hive discussed here, there will be no issues in a standard Langstroth extractor as they use cut down Langstroth dimensions.
The extraction method is described in his book, it is in pages 71-73 in the original French 12th edition and it is also covered in pages 62-64 of the English translation provided by David and Patricia Heaf.
Here are images of the design of the cages from the 12th edition.
This is an example of the extractor, which is essentially identical to the modern day extractors used for Langstroth frame extraction. Warré has specific reasons for suggesting a 4 frame tangential extractor.
I would recommend **_not_** pressing or crushing/straining frames if you are nadiring your hive boxes (adding them from the bottom). When you nadir boxes, they all move through brood laying before they are then used for honey. When crushing/pressing this comb to extract honey, you will be crushing the larval faeces and cocoon remnants ([slum gum](https://en.wikipedia.org/wiki/Slumgum)) into your honey. You can call this 'raw', 'unfiltered' or 'natural', but it is what it is. If you are supering your hive boxes (adding them to the top), and they haven't had brood in them, crushing/pressing won't have the same potential issue.