No, it does not protrude obtrusively when mounted on my camera. Note, however, that I mounted the hot shoe adapter as far back on the mounting rail of the RDS as possible, for exactly that reason. If I am wearing a ball cap in the normal way (ie visor forward), then the RDS does interfere with the ball cap when I try to look through the camera viewfinder. In such cases, I usually just rotate the ball cap so the visor is out to the side or rear, or I remove it altogether. Without the ball cap, I can place my eye up to the camera viewfinder and don't even notice the RDS mounted to the hot shoe. When in the field in an environment where there is a chance of bird-in-flight shots, I often leave the RDS mounted for the entire outing. I don't leave it turned on, though, as that is too hard on the battery. When using the RDS, I like to keep the camera pressed up to my face just as I would when using the camera's viewfinder. Some folks prefer to use the RDS with arms outstretched, but I find this does not work nearly as well for me.
Hopefully it will be the same on your camera, but if not, it is quick and easy to slip the RDS off and put it in your pocket for a few normal shots. It means you're not as ready for a surprise bird-in-flight opportunity, but that's a chance I'd be willing to take. I do not like to use the LCD display on the back of the camera for framing and shooting of handheld shots. If it came to a choice between using the viewfinder or using the LCD display, I would remove the RDS in order to use the viewfinder. I like the intuitiveness of aiming the camera using the viewfinder, and would never buy a camera that did not have an integrated viewfinder. I also like the extra stability of having the camera pressed up to my face compared to holding the camera out in front of me the way you would if using only the LCD display. (On a tripod, however, I will sometimes use the LCD display.)
Good luck with your new gear. It will take some practice to get used to using the RDS. Be prepared for a low success rate initially. You will find, though, that persistence and practice will pay dividends after a while, and your success rate can get very high using this simple device.