Full Resolution Sync from Lightroom Classic 2024

The answer to your specific question is no, not at present?
I you have access to LrC then you are subscribing to the Adobe Photography application and you have the following applications.

PhotoShop., Lightroom Classic (LrC) , Lightroom Desktop ( Lr ) . 
LrC syncs smart previews to the Adobe Creative Cloud  which do not utilize your sync allocation, original images. must be stored on your Computer.

If you use Lr Desktop you can upload original images to the Adobe Creative Cloud which will utilize the storage allocation and you will have originals on your and the Adobe Cloud.

The Adobe Photography Plan costs $9.99 per month with 20GB storage if you require additional storage in the Cloud the cast is an additional US $10 per month.

Having originals on your computer and in Adobe Creative Cloud has a cost.

PS. My though on this is the is no Lightroom Classic is not available as a stand alone application as it was from Lightroom version 1 in 2007 to version 6  in 2015,  it is now only available in the Adobe Photoshop Plan with Photoshop as the primary application, which has Bridge and Adobe Camera Raw plug-in, Lightroom is an alternative to Bridge and Adobe Camera Raw plug-in so it is a free-be in the package of PS, LrC and Lr Desktop for Adobe Creative Cloud for Us $9,99 per month .with 20GB, additional storage US $10 per month for 1TB.