TL/DR
I assume it needs to be directly connected to that pool network? If the pool IPs and the VIP are in the same subnet, Yes.
Most scenarios show AVI connected to a T1 which also connects to the Pool network, can AVI LB for a network that is beyond a T0? Yes
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As states. The AVI Load Balancers are VMs and can be deployed in a number of different ways.
The AVI SE (VM) can have an arm in the pool subnet if the VIP is in the same subnet. This is reminiscent of one-armed load balancing.
Another deployment model is for the SE's to be placed in a different segment and then route to the pool members. In this instance, the SE will use the T1 to route between the VIP and the Pool members. If the pool members are physical DBs, then the T1 routes outbound towards the T0's and further (unless bridged which causes an issue).
N.B. In the 2nd example, the SEs would live on a separate subnet (10.10.10.0/24) and the pool members would live on a different subnet (10.10.20.0/24). Simple routing takes effect here. Take note, the VIPs can be either in the 10.10.10.0/24 range or a completely different range, 172.16.10.0/24 for example. The 172.16.10.0/24 is then injected onto the T1. This is NSX Cloud mode.
This might help:
https://vmusketeers.com/2021/12/06/nsx-alb-advanced-load-balancer-design/
Sorry for the self promotion.