You should look at the question in the eyes of two sides who play the game.
The first is the "Grunting" player and the second is his opponent.
From "Grunting" player side their coaches and trainers sometimes
claim it helps a player's timing and physiological release of hitting the ball.
Nick Bollettieri, seen by many as the world's top tennis coach, and whose proteges include many of the noisiest players, says grunting is natural, not planned.
"I prefer to use the word 'exhaling'. I think that if you look at
other sports, weightlifting or doing squats or a golfer when he
executes the shot or a hockey player, the exhaling is a release of
energy in a constructive way," says Bollettieri, speaking to the BBC
News Magazine. "If you hold your lips tightly, you're not breathing
and you become very tense and less flexible so you get tight more
Louise Deeley, a sports psychologist at Roehampton University explain:
"The timing of when they actually grunt helps them with the rhythm of
how they're hitting and how they're pacing things, It may be
that their perception is that if they grunt, they are hitting it
harder. It's going to give you confidence and a sense of being in
control of your game."
And world class tennis players such as Serena Williams are not alone
in their loud grunts. "When people are exercising on their own,
they'll use things like how they breathe in and out as a rhythm, They may make similar kinds of noises to [the grunts]."
From other side it sometimes can affect opponent's performance.
Tennis great Martina Navratilova summed up the problem with grunting in a Sunday Times column last year:
"It affected my game because to me it is important to hear the ball
hit the racket; you can hear a bad shot before you can see it and the
sound is an imperative part of the game."
A recent study has shown that distracting noises during tennis games can affect an opponent's performance.
33 undergrad tennis players to view videos of a tennis shot being hit
toward them and to quickly judge whether the ball would go to their
left or right.
After measuring their response and accuracy when only
hearing the sound of the ball on the racket, he then introduced an
extraneous noise similar to a grunt at the instant the ball was
struck. The students' response time and accuracy of direction
prediction decreased significantly when the sound was included.
So to sum up I think most tennis players who grunt do it because players simply need to grunt as they swing, it’s probably more relevant to ask if it’s dramatized. Some players might exaggerate their grunts simply to surprise or throw off their opponent.