1st thing, grab that Tremec. good investment.
As to the overdrive trans. I believe it should operate as a normal 3 speed with no power to the solenoid, no matter if the 3rd shifter (lockout) is in or out. I'm pretty sure the lockout only affects operation of the solenoid to engage the planetary set. If I remember there is a sprague clutch that may prevent the output shaft from reversing.
It's been a long time so go easy on me if I'm not 100% correct.