Generally no, but as a professional matter, I have taken to downloading datasheets of components selected in the design, at least when I remember.
A downside to always referring to one version, is missing the errata and other updates, say in MCU data.
A couple of websites I've logged, either for local use (a calculator or two, implemented by clientside JS--how convenient), or for reference. Very few; but in fact
one such reference I've kept online recently caught the eye of its original author, who was impressed to see it ~two decades later.
Backups/history, duplication of data (whether by same, or by being included, in part or in whole, in other files, in the normal process of combining things to create output), and generally accumulating data as the project goes on, can get quite expensive, in a certain sense*. A lengthy project from a couple years ago takes up nearly 900MB; a lengthy current project is now over 2.2GB. Much of which is Altium bloat -- backup/history is saved as whole-file ZIPs, so there's a lot of repetition, especially of bulky items like 3D models.
*A gig is a lot of data, in terms of human senses, I would say. You could pore over that, as raw bytes, for an entire lifetime; or look at it through various views / parsing as the various formats it is. Or, if it were converted to raw video (not that it'd be at all intelligible as such), several minutes worth of modest HD quality.
Tim