Can non-laying older hens effect laying behavior of younger hens?

No. I've had older hens (but they always laid some, even 6-7 years I'd get a few eggs a week from them from spring til fall, none in the winter) and first year pullets, the young girls laid right through that first winter.

 

Hens go through a natural cycle; They spend a month laying a dozen eggs then stop laying for 3 or 4 months while they hatch and raise their chicks, they lay for another month or so then take another 3-4 month break while doing the broody thing. But this type of behavior has been breed out of modern production egg hens
If they were commercial production breeds they all would be considered spent hens and be replaced.
They could also have a feed & nutrition problem such as low protein or calcium.
Depending on their breed your problem could be molt, broodyness, feed, stress or a combination of factors. But it's not the old hen's fault.
My hens are largely game mix and it seems as it they only lay eggs 5 months out of the year.