Would the seating position of a road bike cause issues with prescription glasses
Yes, in most cases normal prescription glasses sit too low on the nose for the purpose of shielding the eyes in road bike position. And as the speed increases, the need for effective eye protection grows, too. Consider either:


Getting contact lenses, and then you can wear bike specific glasses
Getting bike glasses with prescription lens inserts. In my experience, they are somewhat awkward to handle and not all optometrists will undertake fitting the lenses to what they perceive as nonstandard frames.