A user agreement isn't just a "person with account" agreement, in fact, if you read the first sentence of the introduction [1] to their current one, you'll see it says
> You agree that by clicking “Join Now”, “Join LinkedIn”, “Sign Up” or similar, registering, accessing or using our services (described below), you are agreeing to enter into a legally binding contract with LinkedIn
in other words, anyone that "access[es] or us[es]" their services are agreeing to the contract. This definitely includes what OP is doing.
> You agree that by clicking “Join Now”, “Join LinkedIn”, “Sign Up” or similar, registering, accessing or using our services (described below), you are agreeing to enter into a legally binding contract with LinkedIn
in other words, anyone that "access[es] or us[es]" their services are agreeing to the contract. This definitely includes what OP is doing.
[1]: https://www.linkedin.com/legal/user-agreement#introduction