It depends on a lot of things, but off-hand, probably not.
All 360's are externally balanced from the factory. Balance is on the torque converter and balancer/damper.
Cast crank 340 are also externally balanced, on the torque converter and balancer/damper.
But there is more weight involved with the 360 so an OEM converter wouldn't be balanced correctly.
Same situation with forged crank 340's, which are internally balanced. No weight externally, but converter can't be swapped around.BUT if you do have a forged crank, internally balanced 340 with a neutral, no weight converter, you can simply use a B&M flexplate for an LA 360. It has a cresent cut out of it for proper counterweighting.
OEM flexplates are neutral balanced.
Other option is to find an OEM 360 specific converter. (non-lock-up)