Can a dedicated office space improve employee engagement even if some are remote?

I would say that you should add Gamification mechanics, so all of your team regardless where they are could have a stronger and tighter engagement.

If you think of a physical space, you are limiting the view of interaction between all team members and you have to be sync rather than async.

Maybe not office space but something like a club house?  The intent is to get people together in a physical medium.  Maybe not 100% business focused but more about building relationships and team culture.  

No.  Working in teams or groups can be done in three ways - 1)everyone in the same room, 2)some attendees in the room and some remote, or 3)everyone remote.  Best overall engagement is from option 1 and the worst engagement comes from option 2.  

There is utility in having access to office space. However, when remote or hybrid work results in "hoteling" and not having your own office (or desk), that becomes a problem. Having to "book" a space (and ensure you book early enough) is a deterrent to coming in. Also, it feels very different when it's no longer YOUR own office. 

I would much rather work at home, where I have everything I need here, rather than commute in and bring everything with me. 

I think having a "home base" can be helpful. I wouldn't force people to come in. It's silly to go into an office to conduct meetings remotely. But I still feel that an opportunity to have some face to face provides value that full remote doesn't.