If first client takes connection, it will get first stream from first antenna. Second client will get second Tx-Rx stream from second antenna.
No, MIMO allows single client to communicate with double (tripple, quad, ...) speeds. The way you explain is called MU-MIMO for "multi-user" MIMO and that's advanced. In typical cases AP (or 4G/5G base station) uses advanced antenna array which then intelligently adapts antenna pattern into barrow beams to hit client with higher signal strength.
What you're aiming to achieve is usually called "space diversity", but as I already explained not all wireless systems are designed to transmit beacons over all antennae (4G transmits reference symbols over all Tx antennae) and if beacons are only transmitted over single antenna, then clients won't detect wifi AP in vicinity of the other antenna.