May it be possible that the trusted third party knows the parties' private keys in an "ideal model" of a Secure multiparty computation protocol?
Yes.
Trusted party setup is just way to think about what the end goal of a particular MPC system is. So you may start with a party (lets call it the dealer) that sends it's private key to the trusted party, and then the trusted party uses it to commit a transaction.
Now replace the trusted party with a multi-party setup. The dealer here sends shares of its private key to each of the parties. The parties then can regenerate the private key or commit a transaction with it.