I have the following topology for a specific vlan.
The switch named switch-4 has to be connected as per this topology.
Is it a valid design to apply the concept of RTG on this switch (switch-4)in the uplink to switch 2 and switch 3?
If the picture shows complete L2 topo, then RTG on switch4 for green links should work fine.
Switch4 will break the loop by using only one interface from RTG at a time (packets, BPDUs on backup interface will be discarded).
You don't have to disable STP on links between switch1-2 and 1-3. Only requirement here is to disable STP on switch4 for links participating in RTG.
You wrote: I have the following topology for a specific vlan.
RTG is per interface and not per vlan, soeither all or none
if you need quick convergence have a look at Ethering Protection SWitching
or VC or VCF
Yes, If the active link fails, the secondary link automatically starts forwarding data traffic without waiting for normal spanning-tree protocol convergence.