Yes for Adaptive Automaton, no for Metallic Mimic.
The distinction is: Adaptive Automaton has a continuous effect that applies to Walking Ballista while it is on the battlefield, and the effect becomes active at the same time that Ballista enters the battlefield, so Ballista is a 1/1 from the start.
By contrast, Metallic Mimic has an effect that applies a replacement effect to how Walking Ballista would enter the battlefield. Mimic's ability can't apply to Ballista if they enter the battlefield at the same time because the effect has to be active before Ballista enters the battlefield in order to apply.
Walking Balista
Adaptive Automaton
Ok I bring them out at the sametime via an effect like
- defense of the heart
- Victimize
.I name construct on the mimic or automaton?. Would the balista be alive from either of the power/toughness lords?
http://www.youtube.com/watch?v=SY8h2vp5Xis
The distinction is: Adaptive Automaton has a continuous effect that applies to Walking Ballista while it is on the battlefield, and the effect becomes active at the same time that Ballista enters the battlefield, so Ballista is a 1/1 from the start.
By contrast, Metallic Mimic has an effect that applies a replacement effect to how Walking Ballista would enter the battlefield. Mimic's ability can't apply to Ballista if they enter the battlefield at the same time because the effect has to be active before Ballista enters the battlefield in order to apply.
http://www.youtube.com/watch?v=SY8h2vp5Xis