Can a human defeat an engine in a 10-game match if he is given the White pieces and draw odds in every game? What would happen in a 10-game match between one of the strongest human player (Carlsen, Caruana, Aronian, Kramnik or Anand) and one of the strongest engine (Komodo, Stockfish or Houdini), but with the following two conditions:


The human always has the White pieces in every single game.
The human is given draw odds: a draw is counted as a White win (i.e. in the advent of a draw White gets 1 point and Black gets 0 point).


The games are played at classical time control: 120 minutes for the first 40 moves, 60 minutes for the next 20 moves and then 15 minutes for the rest of the game with an increment of 30 seconds per move starting after move 61 has been made.

The engine is run on a powerful computer, gets 7-piece Lomonosov endgame tablebases, has permanent brain (ponder) on, and has a big opening book designed to avoid getting into drawish positions.
In contrast to Rauan Sagit, I'm going to offer some reasons I think any human should (assuming they don't get lucky and play some computer-level games themselves) lose such a match. 


Elo differential: As of Nov.15, 2014, the highest-ranked engine on CCRL 40/40 is Komodo with an Elo of 3303 on relatively modest hardware of an Athlon 64 X2 4600+ 2.4 GHz (Engine ratings were initially based on human ones, but you could debate how relevant it is to compare the two. We have no other metrics, though, so I'm going with this). The all time peak rating was Carlsen's 2882 - let's use him as our example and assume he is able to play consistently at a 2882 rating level. This is a differential of 421, and the central observation of the Elo rating system is that a rating difference of 400 points should correlate to a 95% probability of the higher rated player winning (not counting the possibility of draws). Top GM games draw around 50% of the time, meaning that even if this rate stays the same, Carlsen will be fighting for draws with no practical possibility to push for a win. This means that, at best, you would be expecting him to stand a chance of just winning the match with him playing at a peak level consistently throughout the match.
Time control: If the time control is short, humans are likely to blunder when at best computers will make sub-optimal positional choices. If the games are long, it becomes very hard for the human player to remain consistent until the end of the match.
The engine (assuming the people setting it up actually want it to win) would have it's 'contempt for draws' set really high, meaning it would keep pushing on until the human cracked.
The psychology of such a match (assuming that there is enough of a prize/prestige for the human to be taking it seriously) can be really taxing on the human player. Kasparov-Deep Blue were 6-game matches and Kasparov was finding to hard to maintain his mindset and mental stamina well before the end of these. Of course, there were other factors at play at the time, but a 10-game classical control match is very taxing.


I'd also point out that Rauan's last paragraph suggest a modification that would likely make it too easy for a human player to win. keeping the computer's calculated advantage relatively low after 30 moves should not be too difficult with appropriate opening choices. I think a better adjustment would be that if the score is 0.00 +- 0.05 for at least 5 ply and the human offers a draw, the machine must accept. Either that, or make the match take place over a long period of time, with one game every 3 months or so (in amongst other tournaments) to prevent fatigue.