No—Echoes of Aincrad is single-player.
Steam lists Single-player, Steam Achievements, Steam Cloud, and Family Sharing. Bandai Namco also labels the game Single-Player. The companion fighting beside you is controlled by AI.
Why the game can look like an MMO
The story takes place inside the Sword Art Online VRMMORPG and follows players trapped in Aincrad. That is the narrative setting. The retail game itself does not provide co-op parties, PvP, cross-play, or MMO servers.
How the party system actually works
Before each quest, you select one AI partner. You can adjust the partner's weapon and skills at an Inn and issue Switch Mode or Free Mode commands during combat. Combination Skills and partner support create the two-character combat structure without another human player.
Buying decision: choose Echoes of Aincrad for a solo action-RPG campaign with companion tactics, not for playing through Aincrad with a friend.