Is it true that even if you catch a cold, it is still easy to sing falsetto?

I got this question from a singer who has shown a great kinematic performance of the larynx:
Is it true that even if you catch a cold, it is still easy to sing with falsetto?
I thought, that is a really good question!
The answer is yes, the falsetto is displayed when the thin mucosa of the vocal chord mainly vibrates. Where as the original voice is displayed when the vocal cord muscles and mucosa vibrate together.
If you catch a cold, the vocal chord is swollen due to inflammation, maybe you’ve seen the red intrinsic larynx by observing visually or in a hospital, this is referred to as hyperemia.
The hyperemia is when a blood capillary explodes and the blood vessel gets closed.
The hyperemia weighs down the vocal chord, the vocal chord then swells. The heavier weight from being swollen produces a lower pitch than normal.
Furthermore, it becomes harder to control voice pitch, and the throat is more inept to get dry. Mainly because the blood vessel is closed and in turn creates a reduced flow of blood through the bloodstream.
Additionally, increased viscoelasticity of the mucus will occur, and is usually accompanied by sputum in the back of throat. The voice will sound noticeably shattered or gravelly, because when the glottis opens breath is leaked out.
But, what if you experience barely being able to sing with falsetto?
Cold strains do vary. The mucosa has no blood capillary and is sometimes not affected by the hyperemia. Therefore, it is true that even if you catch a cold, it is still easy to sing falsetto.
Of course, the sound quality will vary when you have a cold.
Please be careful not to catch a cold.
Common colds often cause the larynx to become swollen inside, similar to a musician pouring water over their instrument. What happens is that the wooden parts will absorb the water and will not be able to be played properly.