Can LTM be used to configure Active and Passive Servers?

Agreed, further app details aren't needed at this point -- it is sufficient to know that the back-end app is capable of resuming a session on a new pool member (recovered principle device) from another pool member (secondary device).

SOL7208: Overview of the OneConnect profile https://support.f5.com/kb/en-us/solutions/public/7000/200/sol7208.html

OneConnect cliff notes: Allows abstraction of the client side tcp session from the server side tcp session. Additionally, it allows multiple client side connections within_the_same_tcp_session to be carved up into multiple server side connections (think upstream reverse web proxy; e.g.: Akamai). This OneConnect framework would, in theory, provide the needed hook to redirect the server side tcp session.

It is one of the more complex and sophisticated features of an F5.

To be clear, it is doubtful that a checkbox exists that enables the desired behavior. A useful (needed?) side effect of the OneConnect feature is that the profile enables per packet inspection of the client side traffic which means, in theory (a lot of theory here), that one could evaluate if the principle PGA pool member had recovered and force a pool member reselect once detected.

As such, OneConnect + iRule may accomplish what you're after...

...or cause a TCL error, TMM core, or sundry other possible problems. Be sure to test in a lab (basic fail-over/back during active traffic would be sufficient for a PoC) and load test for performance (anytime iRules are used to solve problems, this is particularly crucial). Making a new LB decision on pool member recovery mid-stream is not going to be a common use case (read: won't be heavily tested by PD nor have the benefit of heavy usage/validation in the field).

Allow me to re-iterate that a solution such as this would really best be addressed by an F5 savvy solution architect.

It may also be worth contacting F5 Support to submit an RFE -- i.e.: PGA higher priority pool member recovery auto-failback feature of some sort; the converse of AoSD Reselect feature, if you will (AoSD = pool feature "Action on Service Down").