Yup, if you have the same address on both wallets (copy the wallet.dat file), and you send a transaction from a pool, it will register on both wallets as soon as they are synced.

You can take that same wallet.dat and archive it, and years later drop it in a fresh wallet, and sync it from the start, and it'll show up every transaction.

The only differences are solo mining and creating new addresses, where blocks can be awarded to a wallet without being assigned to an existing address, it creates a new address.  If you copy a wallet before creating the new addresses, they won't show up in the copy.  If you copy the wallet after creating the new addresses, they will show up.