nope. The problem is that Res sig ONLY recharges when you get a moral boost. There are other options however, echo {E} works well and gives you a permanent 5e, 5 sec cast (echo + res sig) res.
It is indeed possible to echo res sig, and the echoed res signet does function like a normal res signet. I'd imagine it would also be possible to get a third res signet if you had an ally also using Echo, and you used arcane Mimicry to get a second echo.
I was kinda thinking about the echo'd sig all weird. You can echo it, but it only would be useful if you needed to res 2 ppl within the 20 second timeframe of the echo'd copy. Unfortunately, echo does not copy the sig until it has been used so it doesn't really help much that you can copy it.
