BAK. Of course there will be flex. The physics principle in play here is "objects at rest tend to stay at rest". When the bow string pushes the arrow from the rear, the arrow wants to stay at rest, but it can't. It will be pushed forward. In so doing, the shaft will flex, from the force applied to the rear of the arrow as it tries to overtake the front of the arrow, which doesn't want to move, regardless of the orientation of the string, even if it's in perfect alignment with the arrow.
Easton demonstrated this more than 20 years ago with high speed photography. On compound bows released with triggers on arrows that were perfectly centered on the string, the arrows flexed both side to side and up and down, i.e., fishtailed and porpoised. The amplitude of those movements is dictated by the spine of the arrow, the greater the spine, the less the flexing. Because most wheelie shooters shoot very high carbon spines, and their bows are centershot, there isn't a lot of flexing, but they do flex and it is easily detected with high speed photography.
Conversely, the less the spine, the greater the flexing, to the point of the arrow breaking if the spine is way too light. In fact, the myth that you can't/shouldn't shoot wood arrows out of compounds bows is based on that principle. Folks thought, and some still do, that wood arrows aren't stiff enough to shoot in compound bows. Some may not be, but an appropriately spined wood arrow will shoot out of a compound just as well as any other material.
Of course, now we're getting way off the track.