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Yes if upgrading from 2.0 onward.
No if upgrading from any 1.x to any 2.x.
EDIT : Yes. Updating mods during a playthrough is usually safe. When it isn't, the author usually mentions it.
Ummm... Howso? I was under the impression that they were made ESMified ESPs in 2.X specifically for the reason that it would FUBAR load orders if they were updated to true ESMs because of the file name change.
My mistake. You are absolutely right. That was effectively the whole point. Not sure what I was thinking.