The answer is both yes and no. It all depends on the regional variety of English being spoken and the care taken by the speaker.
The phonetic symbols show how this works. A /hw/ sound is spoken differently to a /w/ sound. A /hw/ is evident in the ‘Queen’s English’, as in the word ‘what’. However, even within England the/hw/ is not used in many regional accents, or else it is very weak. The /hw/ is not used at all in Australian English. These speakers simply use a /w/ for both words ‘what’ and ‘watt’.
Try it out for yourself. With the word ‘watt’ /wat/, you start your voice as soon as you begin to say the word. To pronounce the word ‘what’ as /hwat/, round your lips as for /w/ but blow a little puff of air through them before you start your voice. Make the air puff both weak and short. You should have to listen quite carefully to hear it.
The big question is: Should you learn to use the /hw/ sound in your own speech? The answer for most is that it’s probably not worth the effort. Most listeners will be unaware of it and even good speakers may neglect it. If English is your second language, and you are learning many other English sounds, you will have far more important sounds on which to focus.