No. Synchronization happens through iCloud, or through other cloud services (e.g. e-mail providers, other cloud providers). A new phone could synchronize against stuff you had in the cloud or an e-mail provider's servers, but could not synchronize directly against a lost phone that was hundreds or thousands of kilometers away.
Likewise, Quick Transfer requires you to place the old and new phones next to each other, within Bluetooth range.
Unless someone finds that phone, knows where to return it, and is honest enough to return it … and that phone is still in good condition, and hasn't entered a security lockout condition (from too many incorrect passcode entries), any data that exists only on that phone is gone.
Which in practical terms means there is more chance of winning the lottery than of seeing that data again.