You get the sick pay, but are disqualified for holiday pay. What would they do subtract it from your sick hours balance? Otherwise you would just get it at the end of the year.
Can't see getting a letter but you will lose credibility with your coworkers and managers. You never know when you will need a favor and they will remember your sick days. We have people that always call in sick around holidays and are usually out of sick days by Thanksgiving. Nobody is willing to swap vacation days or help them get off early because they always cause hardships on their coworkers.
Sounds like same person at my station. That pre-peak “injured” old fart senior courier in my station finally retired as his manager posted the route for bidding after newer policy of 45 days on injury. He came in walking just fine in plain clothes on Friday 21st bragging his retirement. I told him good luck being a Walmart greeter.