If I insert the Pokemon Black 2 cartridge into another 3DS will the save file be deleted

Well, you can't over write the save that is already on the game, which you got the warning message about when it said" "please press SELECT+UP+B at the start menu." so, if you want to save in game you have to start again and follow that command to be able to save after.

With the legit version of black I had the same problem, I bought a 2nd hand version and I got to the first gym and couldn't save, I had to restart the DS delete the save file and then I was able to save.

Direct Answer

No, you can't you have to start the game but before you can start a "New Game" you have to follow the "please press SELECT+UP+B at the start menu." command

P2 Laboratory (or P2 Lab) is a small island with a lab on it. It's located in South Eastern Unova. The only way to reach it is by going West on the Southern half of Route 17, North on Route 18, and East on the Northern half of Route 17.

Inside the Lab is a Scientist. If you have a Genesect, the Scientist will challenge you to a battle.

TAKE NOTE: The following are the Pokémon that the Scientist will use. There is also a chance of him using an X-Special in the battle.

The Scientist may use an X-Special in this single battle.

Klink ||| Klang
Level: 34
Type: Steel
Ability: Plus or Minus
Hold Item: N/A

      Moves

• Gear Grind

• Bind

• Charge Beam

• Autotomize

After the battle, he'll give you two Drives for Genesect's Techno Blast. The drives depends on which version you're playing. Black 2 gives you the Burn Drive and Shock Drive. White 2 gives you the Chill Drive and Douse Drive.

A Dubious Disc can be picked up in the back of the room.

All this with reference to: LINK