It's difficult to answer with only one character concept presented, but an alcoholic mercenary who hates their own race, while it may seem fairly one-dimensional, does offer a lot of potential for growth. Here are a few things to explore with that character:
- Why exactly do they hate their race? Is it due to the race's
expansionist tendencies, or was there some trauma that occurred to
Does the character have any family? I would recommend requiring your players to have at least one or two plot hooks you can exploit
built in to their characters' backstories. (e.g. for the alcoholic,
perhaps they have family that still lives in the empire, and they
drink to beat down the feeling that they have abandoned them. Maybe
one day they receive a letter from that family begging them to come
- Where is that society expanding to? Will they be in an area near your party? Maybe your party comes across a warband belonging to that
race and the alcoholic character is forced to confront a figure from
their childhood, eg a prominent public servant, a lieutenant that was
stationed in their home town, a childhood friend who grew up and
joined the army (why did the two of them split so drastically?)
If your group is as creative as you say they should have no trouble (and even a lot of fun) coming up with such things, and any time the campaign starts to slow you can pull something from one of the characters' backstories to get things going again.
As far as stats/classes go, those can be much more difficult to address, as generally more creative players are more resistant to their character concepts being changed. Often the best thing you can do is look at what the player wants their character to do, and suggest an alternate class that may work better, and possibly implement stat minimums (for instance a thief not having a dex or int lower than 12 as they must be agile and clever to survive in their chosen profession).
While I have only played 4e a handful of times (I would recommend 3.5 or Pathfinder over 4e any day, but that's getting more into the realm of opinion), I do recall a certain paragon path for the fighter class which may fit your alcoholic thief called the pit fighter (or something to that effect), so if you can persuade them to be patient enough to wait until they are a high enough level to choose a paragon path that may work for them. Otherwise there may be other classes put out in supplemental books that fit better since the last time I looked at 4e (which was shortly after the original 4e player's handbook was put out, so that is well within the realm of possibility).
Even with doing these, your players may still find ways to make their character concepts unviable. Players exist to make the GM's life hell. In that situation, there is really nothing you can do but tell them that if they insist upon playing that character it will most likely die very quickly, and the character's in-game actions will have in-game consequences the player may not like. The character will likely die within the first few sessions, but the player may be willing to reroll a more practical character after watching their concept crash and burn.