(Added 7/19): It should be pointed out that this is not even in question.
Petr Korda's tennis career took off when he used steroids. He won the Australian Open and made the Quarterfinals of Wimbledon, when he was found to be positive. 16 year old
Sesil Karatantcheva came out of nowhere and managed to beat Venus Williams at Roland Garros, then tested positive for steroids. There can be no doubt that steroids will help a tennis player, male or female to perform well beyond what they could do without steroids.
Nevertheless, the argument that steroids won't help a tennis player has been put out there on several occasions. The general argument is that tennis is a game of hand-eye coordination, strategy and placement, none of which would be helped by steroids. The other point is that there is no direct correlation between a muscular player and the power of their serve, so bigger muscles wouldn't even help the serve.
In actuality, steroids help in the following ways:
Strength and Power: Powerlifters add easily 20 -30% more to their lifts on steroids. (You can check this by comparing the drug-free powerlifting records to the "untested"). That makes for a significant amount of power to your tennis game.
Speed - Track and Field athletes are probably 5% faster on steroids (I'm talking about the difference between a 10.0 and 9.5 second hundred yard dash).
Endurance - I won't put a number to it, but clearly if Tour bicyclists are using steroids, it is helping them with endurance. Otherwise any gains in strength would be negated by the long distance of the events.
Longevity - Baseball players were suddenly able to compete at a high level even into their 40's.
So, on steroids, you are going to get and athlete that is stronger, faster and has better endurance. All the top athletes have great hand-eye coordination, great placement and strategy. While there may be a difference between one player and another - enough of a difference to win most times, all things equal -that will be easily overcome if you are faster, stronger and have more endurance than your drug-free opponent. It's simply no contest.
Let me also address the service issue. While it's true that the service motion is not just a display of strength and there is much more to serving a tennis ball than raw power, that doesn't negate steroids as an aid to a serve. Just as steroids are going to help a baseball pitcher (just ask Roger Clemmons - I dare you), they will help a server. The motions are similar. Your medium quality server will become a good server. Your good server will become a great server.
Now, is there a disadvantage to steroid use for a tennis player? There is one disadvantage, as I see it: The increase in bulk. The 'roided up player is carrying around a extra weight. However, this appears to be offset by the strength, speed and endurance gained. This might be why we are suddenly seeing very large players able to compete on a tennis court, players like Serena, Kanepi or Bartoli on the women's side. You would not have seen a women with a physique like Marion Bartoli winning major tennis events in the past. In my opinion, it could be that performance enhancing drugs allow someone of that size to maintain a peak game for 3 sets of tennis.
In short - YES - Steroids are going to help a great deal.
Update: I now see some are suggesting that
steroids even help hand-eye coordination.