Sure. Depends on a lot of factors.
Our equilibrium can be affected by congestion and inflammation in the sinuses and ears; by our vision, particularly astigmatism; distortions in eyeglasses -- common with no-line bifocals, cheap sunglasses and even good quality wraparound lenses -- and in transparent windscreens on motorcycle windscreens and automobile windshields.
Our balance and ability to change directions can be influenced by uneven arm and leg length (more common than most folks realize), injuries, joint degradation, etc.
Recently I felt some oddities in my '89 Centurion Ironman. I noticed the headset kept loosening. Rather than fixing it properly -- disassembling, inspecting, repairing/replacing -- I just snugged it down and cranked on the lock ring. Now it has a very notchy feel, so it definitely needs an overhaul. While it wasn't ridden much before I bought it in 2017, it wasn't stored very well so I'm sure the headset needs work.
A poor bike fit or makeshift changes to suit comfort without regard to balance can affect how our bikes handle. Due to pretty serious neck and back injuries from being struck by a car almost 20 years ago, I had a really hard time adapting to any bicycle back in 2015 when I resumed riding. For the next three years I made changes to my bikes to suit comfort first, including shorter stems and higher handlebars.
Then I was hit by another car a couple of years ago, re-injuring the neck, shoulder and hip. Once again, I had to resume PT and it's a daily thing now just to keep the body limber.
As my fitness improved and I got faster, those compromises made the bikes feel twitchy, especially on fast curves and rippled pavement. So I worked on physical therapy to improve my strength and flexibility. I switched my bikes to longer stem and modified the overall fit, so they feel more stable now, although there's still some cost to comfort.
Cable/housing can affect bike handling too. The effort to improve aerodynamics and cosmetics led to some cable/housing routing that can affect bike handling, especially on slow, tight turns. While my hybrid with swept bars and bar end shifters is a pretty good compromise between comfort and responsiveness, the long swept bars and shifters can knock against my knees on slow, tight turns, which makes that bike tricky on some group rides with inexperienced or careless cyclists on some trails.