Generally when I shop guitars I play them unplugged, get a feel for the natural responsiveness, and then plug in to a low wattage amp clean channel. Is this still a good approach for a Les Paul?
I would skip plugging into a clean channel altogether. At least when making the decision. I mean, if a guitar has the resonance and the tone unplugged, you can just change the pickups to fit whatever you want. If a guitar does not have
it acoustically, then you'll just be polishing a turd by changing pickups.
That's just the way I see it, though. I'm sure people will have other opinions.
I mean, it's obviously fun to get to hear the guitar plugged in, but when I bought my Les Paul Tribute, it came with the crummiest pickups ever (490R/490T). But acoustically, it just rings. So I just swapped them out. And I've had good luck, because whatever I've put in it, it's sounded good, just to varying degrees.
Also does it need to be a Gibson/Epiphone or can the copies also have “it”?
Depends on how "authentic" (LOL) you want it. I feel even Epiphones don't quite nail the Gibson experience. I own the highest-end Epiphone Les Paul and the lowest-end Gibson. But it's still a different thing. For me, it's down to three things. First, the placement of the pickups in general is slightly different on the Epi. Particularly, the bridge pickup. No way they can sound the same when the pickup is picking up a different part of the string. Second, the wood they use. I wouldn't go as far as to say one is better than the other, but what is a fact is they're certainly different. Not the same species of Mahogany. Third, the finish. And I'm sure there is debate on how much of a difference this makes. But I find it does, just not nearly as much as the pickup placement, TBH.
If you're spending Epiphone money, I would much recommend you take a look at the more traditional offereings by Schecter or LTD. Much better guitars for the money, TBH. Not to say Epis are bad, but they are not as well-spec'd as the higher-end Schecters and LTD's and are around the same price range.
That is if you're buying new, if not, many of the Japanese copies have a very good reputation. I've never played one, TBH.
That's also me being picky, TBH. I've had and tried a couple LP-shaped guitars that have sounded really good. LTD gets my top recommendation as far as budget LP-types go, personally.
If your budget is higher than that, I would look at Heritage, PRS, or Gibson.
But if you shop Gibson, make sure to try them before you buy. Gibsons are REALLY hit or miss. Some of them are magic. Many of them aren't.