Connecting DAQs in Parallel
Probably not without some means of isolating DAQ0. Even though it may be disabled, it could still take a significant amount of current from DAQ1's output and possibly one or both could be damaged. This is the worst case scenario.

I'd use DAQ1 to announce itself to a relay which breaks DAQ0's connection thus allowing DAQ1 to have full control over the target.

I'd use a relay that switched both ground (0V) and hot too. This keeps them isolated and fool proof.