Altium doesn't care, you are course free to do it however you like.
The three schools are something like:
1. Generic parts. Add the supplier info on the schematic. Never update from libraries.
2. Library part per component type / supplier / etc. Quite tedious, but can be justified when extensive reuse is made -- if you're making dozens of designs per year, say, this can be worthwhile. Can make BOM/alt changes on library level and push to SCH*.
3. Library part per database item. Optional, integrate with inventory database to obtain part, availability and other BOM data (including preferred and alternative parts) on placement, or live on BOM generation. This is the "enterprise grade" solution, a lot of work to set up but it means your production chain is better prepared, from start to finish, with selecting, procuring and storing parts for whatever comes through.
For my part, as a small design shop, I use #1 for most things, with #2 when it's specific parts with few alts, mainly ICs.
*Mind that updating SCH removes any specific attributes you've set, so can screw up things like comments, text label positioning/formatting, etc. Another reason I prefer not to do it.
And you can always go back and copy-paste from some other design, if you've used a particular part before, to avoid entering its data again. (Not like it's a copyright/IP concern, those aren't nearly so fine-grained, component/block reuse is absolutely normal.)
Tim