Yes, but it might take a little longer, especially if you are on the consoles. But since the golden key chests have a much higher chance for better loot, YMMV. You have to spend all of the keys you have, but then when you restore your backup save (it saves your profile, not your character/item saves) you get all of the keys back, yet keep the items you looted or sold from them.
I just hit 28 and am near the end of Eden-6, and I've been doing the majority of side quests along the way. Just not all of the map challenges. I would assume level 30 - 32 is about what most would hit through their first run.
There's no way, without liberal grinding to hit the cap on a first run, unless there's a
huge XP bonus for multiplayer. The map challenges give a decent amount of XP, but it might be faster just to finish the game and move on to hit 50. On top of that, I've consistently been within a level or two (plus or minus) of the enemies for any new given area I've gone to, and when you exceed one level above them, the XP they give diminishes quickly.
edit: Don't know if enemies happen to scale with your level the first time you enter an area, but that wouldn't really change much. They definitely do not scale once you return to the same areas later, and the loot seems to remain a static level as well, regardless of your own.