Does the ship saved by the Bio Integration Circuit get rolled on the turn the Circuit is used?
The first thing that happens on a normal turn is you pick up all of your ships, including any in the Maintenance Bay, except that a ship at the Terraforming Station goes to the stock.

In order for the Bio Integration Circuit card to move a ship from the Terraforming Station to the Maintenance Bay, it must happen before this phase, as otherwise your ship would no longer by at the Terraforming Station. Hence the sequence must be:


Play the card
Move the ship from the Terraforming Station to the Maintenance Bay
Pick up all of your ships, including any in the Maintenance Bay


So yes, you do get to use the reclaimed ship on the turn that you play the Bio Integration Circuit.