Please be careful, the snapshot will complete successfully, but I don't think you have a valid backup. You will not be able to use VSS with the 8i dbms and I'm pretty certain the VSS compatibility for 10g requires patchset 10.2.0.3. You say you are at 10.2.0.1. Just giving you a heads up to test your backup as it may only be crash consistent and to be careful with db corruption (don't select VMware quiescence).
For pre-10.2.0.3 you will need pre-freeze/post-thaw scripts as mentioned in the link Gostev provided.
You can test reproducing snapshot errors by going to VMware and issuing a snapshot, unselecting memory and selecting quiesce. That will simulate the Veeam snapshot.