First off, welcome to TSB.
Is that a vinyl or plastisol transfer?
As for pressure, yes, that would "telegraph" more of the fabric's texture as could really any of the "big three"
Pressure
Temperature
Time
So, yes, while pressure needs may change from garment thickness to garment thickness, some fabrics also are inherently smoother and will obviously produce a smoother print.
One doesn't want to overcompensate with too little pressure and risk good adhesion.
Besides, many actually prefer the look of the fabric's texture coming through a bit.