For sure not. The "cloning" is a feature of vCenter and its nothing more than creating a copy with the option to modify the origin of the inside OS (sysprep). It starts with a VM snapshot which is exactly the timestamp of all your data which will you see in the new VM. If your Source VM gets incoming data this data will not included in the Clone which created by vCenter.
Veeam B&R can do something what youre asking for because it stops the Source VM and the end and merge the Snaptshot data into the Replica. Do you have vSphere Replication around?
Iam pretty sure a that you can do similar by hand.
1. Create a new VM with same specs as your source VM but without vDisks
2. Create Snap of the source VM
3. use vmkfstool to "clone" the vDisks to the new location
4. Shutdown the source VM
5. Modifiy the descriptors of the Delta Snapshot and point them to the new clone one. May its safer to copy the Deltas to new location also
6. Add the Snapshot vDisk (not the cloned ones!) to the new VM
7. Fire it up... if it works consolidate the snapshot
Regards
Joerg