If you play Undertitan and give all units +2 for the turn, if you play a unit from your hand on the same turn after you play Undertitan, does it also get +2?

No, the new unit will not receive the +2 Might bonus.

According to the official RiftJudge FAQ #4537, Undertitan's ability "When you play me, give your other units +2 [S] this turn" only affects units that are already on the battlefield at the moment that triggered ability resolves.

Here is the breakdown of how this interaction works:

1. Playing Undertitan: When you play Undertitan, its "When you play me" triggered ability is placed on the chain.
2. Resolution: When that ability resolves, it identifies all "other units" you currently control on the battlefield and grants them the +2 Might bonus for the remainder of the turn.
3. Subsequent Play: Any unit played after Undertitan's ability has already resolved was not present when the effect checked for targets, so it does not receive the bonus.

Because Undertitan's ability is a one-time triggered effect that resolves once, it does not create a continuous effect that would apply to new units entering play later in the turn.