Possible? Most definitely. Feasible? That's gonna be the key here. A project of this scale is going to take a dedicated team several years. If we had large, organised group that knew what they were doing, it might get done in a year, at the best estimate. Realistically, several years. This isn't a conversion or jest prettying up the existing game. We're recreating the game using a different engine. Things like the sound clips can be re-used pretty easily and effectively, and the modeling, texturing, and level construction will also be fairly easy. Animations are gonna be the big deal here, as will the AI programming. I haven't done anything that involved, so I don't know what's required there. Nor have I worked with Source (I'm surprised no one's mentioned the Unreal engine, which is also free to use for community-made games). Without much more research, I cant begin to estimate what will be required in terms of the physics, particle effects, etcetera.
This project needs strong leadership, a large and somewhat-experienced group of people, a cohesive structure with some kind of schedule. To be truly effective and to move at more than a snail's pace, it will take every active user on this site. If you have no experience with modding or game development, then you can gather screenshots and perform research. To give an example, let's look at the 3d modelers. The modeling team will consist of a master modeler who has a lot of experience and is really good. He will be responsible for the big things, like character models and vehicles (most modelers of this calibre are also experienced in animation, rigging, etc.) Under his direct control are the average modelers, people who are good but not the best. They do the majority of the work, making buildings and props and the like. Each of the average modelers is responsible for a few beginning modelers, people that can work the program ok and are decent at some small stuff. These guys and gals are the ones that get to model the distant objects you see on the horizon, maybe some simple buildings and things, plus they get to critique and check over the other modelers. This way they can see what the higher-skilled people are working on (and they can learn from it), but they can also make sure there's no errors, like open or floating faces that shouldn't be there. Below these are the generic helpers that don't have an technical skills, but can provide ample screenshots and research that will aid the modelers in their task. Earlier I mentioned there's a master modeler controlling this big team; well he reports to the Graphical Lead, who reports to the Project Manager(s). There's a reason that video games have a rigid hierarchial structure: it makes life easy and it gets the work done. A community based game is going to have to follow a similar structure in order to make such a huge project work.
Will this project be easy? No. Will it go smoothly? No. Can the 405th pull something like this off? Yes. But there will be setbacks, it will take a while, and there will be a tremendous amount of work involved. We must have a core group who can see this through to the end. People must understand that this project will be like a second job, and it will eat through your spare time, and it will cause a fair amount of stress.
So ask yourself: Is remaking Halo 1 just a nice fantasy, or is it a real goal that you're willing to put a lot of blood, sweat, and tears into?