Not only is it possible, but PvE has made up the overwhelming majority of my gameplay for the past month.
What have I been doing with all that time? A whole lot of stuff, and little of it directly related to PvP. I say directly because playing the market in an MMO with a player-based economy is certainly a form of PvP. And hey, securing a plot of safe-zone land in ArcheAge is occasionally PvP, too, given how would-be landlords usually bring a friend or two to spam /duel requests or guild invites at competing players, thereby making it impossible for the unsuspecting to be johnny-on-spot when a scarecrow goes down.
Pro tip: Bring your own friends and click the auto-decline duels/invites boxes in your settings. Also, if there aren't any players crowding around the scarecrow waiting for it to expire, keep it that way. Don't be that guy who starts the line and basically puts up a sign that screams, "Hey, come clickfight me for this expiring plot!" in big neon letters.
It's not my favorite thing to do simply because I've done it in every other MMO in the history of ever, but it gets the job done in terms of leveling and it's a good way to ease into a night of sandparkery if there's nothing better on tap. Most nights it's also a great cure for my insomnia, but your mileage will almost certainly vary.
After questing has run its course, I'll craft a trade pack or three, hop an airship, a sailing ship, or a donkey, and deliver various goods to distant lands. This is how I'm making most of my money currently, and once you work out a few optimal routes, it's an extremely chill method of passing an hour and change. I typically read the ArcheAge forums and/or a novel while I'm traveling, though I've also run into tiny bits of roleplay along the way.
Thus far roleplayers seem to be an extreme minority in ArcheAge, which is saying something since they're already a minority in more typical MMOs. Maybe I've just missed them, or maybe they've been incorrectly led to believe that AA is a gankfest. Whatever the reason, the game -- particularly its leisurely trading system -- could do with some more of them.
After I've done a couple of milk runs, I usually either do my post-30 gilda star dailies, or if my mates are about, we'll try our luck at slipping into enemy waters for higher coin and gilda star trade run payouts. This involves transoceanic travel and a certain amount of risk. As I've written before, though, it's quite a good time even when things go awry. Lately it's been going off without a single death, thanks to judicious use of stealthing skills (you can turn in your trade pack without breaking the level 25 Shadowplay version of stealth), diving helmets, familiarity with various harbor layouts, and of course voice chat and good coordination/situational awareness.
Typically I'll end a session by sailing to my aquafarm and harvesting/replanting followed by a teleport to my land farms provided the associated conflict timers are cooperating. A couple of nights per week I try to do dungeon runs, too, both for the gilda star daily payouts and to help lower-level friends get their mentee quests done.
I'll also stop all of the above every so often in favor of a little fishing time. I did a lot of it in recent weeks as I was focused on getting the skill up to 10,000 as quickly as possible. Now, though, I'm angling at a slower pace since I'm saving gilda stars for a fishing boat anyway and I'm no longer itching to power through the newb tier at all costs.
And of course this is just my personal itinerary that we're talking about here. The beauty of ArcheAge is that there is a lot of stuff to do. Much of that stuff is in fact PvE, and XLGAMES has spent a lot of time and money polishing those components to a shine that's comparable to the PvE in the highest quality themepark MMOs.
Jef Reahard is an ArcheAge early adopter as well as the creator of Massively's Lost Continent column. In it, he chronicles one man's journey through XLGAMES' fantasy sandpark while examining PvE, PvP, roleplay, and beyond.