I'm sure there are some who will try, but I think it will take an exceedingly long time.
They've said that the leveling rate will be similar to Skyrim. I think I put about 230 hours into my main character, and I don't think I quite reached level 50 (It's been a while since I've played, so I'm not totally sure what level I got up to). Now granted, leveling slowed down for me once I maxed the skills that I most actively used. The Fallout system doesn't rely on use-based skill increases to bump general XP, so the rate may be a little smoother, but it still gives us an idea what we can expect.
Early levels may come quickly, say 30 - 45 minutes of gameplay per level. That will probably slow to 1 or 2 hours per level once you get past some point (let's say level 10). As we progress to higher levels, I expect that it'll take longer and longer to gain the next level.
As a rough guess, I'll suggest 25 hours to reach level 20, 50 hours to get to 30, 100 hours to get to 40, 200 hours for 50, etc. I would expect that to get up into maxed-character territory, you're looking at thousands of hours of play. Leveling may slow down even more once you run out of quests to do, since Fallout 3 gave a lot of XP for completing quests versus what you could get from combat.