Yes, doing proper breakfalls in judo competition means you increase the likelihood that your opponent will score and achieve higher scores for a given throw.
Noted judo coach Gerald Lafon has made a lot of noise about how this presents the competitive judoka with contradictory goals:
Certainly, the most costly exercise in Judo in terms of wins or losses is the yoko ukemi with arm bash, which results in a full point.
Lafon espouses the use of unorthodox ukemi:
For the last twenty years, I haven’t taught my students how to do ukemi, at least not the traditional ukemi one thinks of when the word is uttered. Modernists call that form of ukemi mat bashing. If you ask many Judo people in Southern California what they think of me, the very first thing out of their mouths is “he doesn’t teach his kids how to fall” as they roll their eyes and imply that I am crazy.
Regardless of why traditional ukemi is what it is today, many modern participants in Judo, especially competitors, resort to all sorts of maneuvers to prevent falling on their back. For the most part, these skills are developed without the benefit of structured class training.
He explicitly teaches turn-outs, under-rotation, over-rotation, and other methods for avoiding landing on one's back in shiai. The benefits of this approach can be debated for the recreational judoka, as can the prioritization of this for the competitive judoka, but acrobatics have potent results in competition. Gymnastics are an addition to your first lines of defense against being thrown (grip dominance, footwork, hip blocks, drilled counterattacks, balance) and less-preferred ways to prevent throws (straight-arming, direct resistance).
Remember, though, that the purpose of taking a fall is to avoid injury. The degree and frequency with which you refuse ukemi is directly correlated with risk of getting hurt. I've sustained moderate injuries because I decided to fall on my front rather than get turned over by a sumi-gaeshi. That's a risk I took for a major competition. Decide: how much injury am I willing to risk for this match?
Shiai is not randori. Your job in randori is often to take your opponent's throws. Your job in shiai is to defeat the opponent, only taking his throws when you are legitimately forced to against your will on fear of injury. Adapting to this might take a few competitions. I recommend competing frequently, particularly in local competitions, to thoroughly learn this lesson.
A competitor's randori should include at least some rounds that are more like shiai, where you demand a much more effective throw to take ukemi from a partner's waza. If your club has them, you can also practice by training harder and more uncooperatively with some of the more fit and vigorous competitors in your club. Do not do this too much, do not do this with new students, do not do this to the degree that higher ranks see it necessary to bury you with makikomi so you stop being overly competitive inside the dojo.
But whatever you do, don't go to shiai and take a fall the way you do in class. Play loose, but stay uncooperative. This is one of the most powerful benefits of hard, competitive martial arts: you must learn to fight hard without being stiff, and to apply technique vigorously against a fully resisting opponent instead of a somewhat-cooperative fellow student in class.