Oh heck yes it is, I do it all the time (albeit never at a level higher than Monarch... I wouldn't want to try it on Deity, that's for sure). I will typically do either Space Race or Culture. Diplomatic is not infeasible, but doesn't really appeal to me. Religious victory would actually probably be the easiest, but again, doesn't appeal. Domination defeats the point (because it involves getting lots and lots of cities) and Conquest would take forever.
Here are some tips:
1. Aim for as many cities are necessary to construct National Wonders (this is 6 on standard maps). This will make your life a thousand times easier, as NWs like Oxford and Wall Street are even more essential in small empires. If you're going for Culture victory, this also applies to cathedrals.
2. Diplomacy, diplomacy, diplomacy. Because you don't want to go around accumulating cities, war doesn't really benefit you all that much. Try to remain on good terms with other leaders as much as possible. Not only will this help you escape wars, it will also open up a lot of trading options for you (a small empire usually means a number of resources will slip through your grasp - luxuries especially are always worth picking up).
3. In my experience, PHI is the best trait. More Great People faster will allow you to compensate for the weaker economy you'll have as a result of having less cities. Get your Libraries (and eventually the Great Library) up and start pumping out Great Scientists like there's no tomorrow. As a corollary, consider running a Specialist Econ more often than you might ordinarily
As a result, the best leader for a small empire game, IMHO, is either Lizzie or Freddy, depending on if you prefer FIN to ORG. I personally think that in a small empire, FIN is more beneficial, but I usually end up playing as Freddy anyway, because historically I think he's a cooler figure LOL (and besides, FIN is weaker in an SE, which I just advocated above).
EXP and CHA are both alternatives to FIN and ORG, as they will help you to grow larger cities. This is especially nice, as the entire point of a small empire is having a handful of massive, powerful metropolises, and if extra health or happiness means you can grow a pop or two more, then all the better. This would make Lincoln and Peter the other two options. So, no matter who you choose, don't expect the UB to be a game-changer
4. Don't neglect your military! This is the easiest thing to do in a small empire and you can get punished heavily for it. Have a city or maybe even two that are dedicated unit-builders.
5. One big benefit I've noticed about small empires is that because you're not dumping tons of hammers into Settlers and losing all your money from acquiring new cities, you get a brief window where you've got a huge advantage over the other players in terms of research and production. Exploit that wisely, and you will go far. What you want to do depends on the map and other factors. I find that it makes early wonders a great deal more viable - but is that always the best use of your hammers?
Those are just a few tips I could think of.