When a new default route is added to the AWS Transit Gateway and if the on-premises will try to reach cloud vCenter through the policy-based VPN, the traffic gets dropped and there will be a routing issue in the NSX T0 router. This is expected behavior.
1. Check for the reply from the VDI machine if it is reaching cloud vCenter by performing a ping test.
2. Check with on-premises networking for reverse tracert.
3. List down the tracert output of the existing configuration (without the Transit Gateway default route).
4. Cross verify if there is a routing issue in the NSX T0 router when the default route is being advertised.
5. Have the Transit Gateway re-added in with the default route and re-attempt the tracert from cloud vCenter to test the machine in order to get a better understanding of the routing path.
The alternative (preferred) solution, would be to migrate the policy-based VPN to a route-based VPN.
In case the Direct Connect (DX) is available, the DX can be used as the primary route that will propagate the Border Gateway Protocol (BGP) routes when the default route is added through the AWS Transit Gateway, and as a backup, the route-based VPN can take precedence in populating the BGP routes if DX were to have any connectivity issues. This is when the "Use VPN as a backup to Direct Connect" slider in VMC UI is selected and switched to "Enabled", and on-premises VDI workloads will still be able to route to cloud vCenter through the AWS Transit Gateway with the default route added.