I have experienced it first hand that winnning awards DOES INCREASE ARBITRATION DEMANDS. Here's my example:
Alex Sullivan, SP, Overall rating 79.
Jaime Butcher, SP, Overall rating 81
Quilvio Guardado, SP, overall rating 83.
In season 16 Sullivan won the Cy Young, and his arbitration demand in Season 17 was $1.7 Million, while Butcher, who is 2 overall points better only demanded $1.6 and Guardado, 2 points higher than Butcher and 4 higher than Sullivan demanded $2.0 Million.
In Season 17, Guardado won the Cy Young. His arbitration demand skyrocketed to $8.4 million In Season 18, while Sullivan asked for $5.2M and Butcher $5.7M.
I believe, from this small sample size, that awards raises the arbitration price for the following season, but it doesn't appear to raise the price for subsequent seasons, because if it did, then Sullivan would have asked for more than Butcher in Season 18.