I dont see how. A lot of that Halo CE feeling for me was about graphics, the Xbox was new and doing things PS2 let alone prior systems couldn't dream of on console. There was a lot of wow factor there. Of course it wasnt just about power but the good design of the art and graphics and levels and AI. It was also for me the first actually enjoyably playable FPS on a console, of course allowed by dual analog sticks (I was coming from Dreamcast and it's single stick). It was the first time I ever experienced a feeling like being in a squad with fellow AI soldiers. So many new things. It just was a brand new experience in a lot of ways.
For a new Halo title to get anything close to a similar reaction for me I think it would have to be a launch title on a super powerful console that was first in it's generation. Not only that but they would have to have a mostly strictly enforced media blackout prior so that I didn't spoil it all for myself in vids (so, basically impossible, heh). Even if it pulled off those things, it would likely still be based on tried and true Halo/FPS gameplay rather than be anything "new" to me like CE was, so it's impact would be dulled there.
Halo CE came out on 2001, I think that was around the time I got my first PC and really joined the internet. So IIRC it wasn't spoiled by vids (I was probably on 56k then anyway).