Yes! After you complete the core memory sequences, you're left in Rome with the ability to go back and play all side missions, Romulus lairs, and collect feathers, flags and treasures.

However! There are at least two things that you cannot do, both because of the same limitation: Once you've finished the core memory sequences (in fact, halfway through Sequence 08) you can no longer visit Monteriggioni in present time—the "Leave Animus" option disappears. Because you can't play as Desmond in Monteriggioni, you can't find the 5 hidden artifacts and you can't access Desmond's e-mail to earn the "Mailer Daemon" Achievement / Trophy.

You need to pause the game, leave the Animus and explore Monteriggioni as Desmond. The five hidden artifact locations are detailed in the side missions section of this guide.

See: 5 Hidden Artifacts in Monteriggioni

The description states that you must kill enemies stationed at guard posts, which means enemies that are not patrolling around. You can find stationed guards during the missions "French Kiss" and "Trojan Horse" during Sequence 06.

See: Guild challenges guide