For installing third party items some dealers will some will not.
Depends on the dealer.
As for buying a car one place and taking it to another... I have done that no problem.
Usually it is because the preferred dealer did not have the car i wanted in stock.
The service dept does not care where you bought it!
Only if that selling dealer had a 'free loaner for service with new purchase' when servicing.. then only that selling dealer would give you the free loaner. Or other freebies.. like free oil changes.. etc. That is a dealer thing. and no other dealer is going to honor it.