After years of observing figure skating both live and on TV, I would definitely have to say "yes". It does affect the judges' scores. That is just a fact, to me, that is part of the sport. This sport has a lot of luck in it, as do most others. One of the luck factors is how the audience reacts to a skater and their program. Another luck factor is if the airlines lose or don't lose skates, or deliver them on time, if they are misplaced. There are many luck factors in this sport. Even the audience reaction is a factor that has multiple parts to it. Does the audience like the music, is one example. Is a significantly large part of the audience loudly rooting for a skater because of national origin, is another. How much does the audience know about skating skills, is another. Is the audience applauding for drama and attitude, is another. Not all audiences have similar composition, too. It depends on multiple factors (there we are with those darn factors again lol), such as location of the event, date of the event, cost and availability of good seats, who will be skating in the event, etc. The composition of the audience itself is influenced by many things, and the reaction of the audience, again, is influenced by many things. There is simply no way to make it all objective and equally supportive of all skaters. It is what it is.
I am glad that eastern Asia is participating in figure skating so whole-heartedly. Various skaters have mentioned how responsive and enthusiastic audiences have been for them when they performed in Asia. I think that an uninhibited show of support does help skaters.