Yes, you can. Web archiving sites like archive.org and archive.md are basically just streamlined interfaces for
WARC recording and playback. They spin up a browser and record what happens when it visits the URL you submitted.
If you record your own WARCs locally then you can log in or do whatever crazy shit you want, because you have full control of the browser. One cool thing about local recording is that it isn't limited to a single URL — if you start the recorder and just browse around normally, it'll automatically archive every page you visit until you stop recording. It'll bundle all of the archives into a single WARC file, but you'll still be able to view each archived URL individually and split into separate WARC files if...