If you want to watch stuff like CNN and golf, then it will be OK for daytime viewing. But programs with any dark scenes at all will be unwatchable with any significant amount of sunlight. Even if you get yourself a 10,000 lumen projector it won't help. The problem is that the darkest part of the picture can not be any darker than the ambient light in the room. So if you have a ton of ambient light the dark parts of the picture will look white or at best light grey and not black.
A black screen or something like the da-lite high-power are designed to reduce the effects of ambient light by reflecting it somewhere other than into your eyes, but they can only do so much.
The other problem with a super-bright projector is that typically they don't look good with the lights turned down, the market is bifurcated - bright projectors for business uses like powerpoint presentations, stuff that doesn't have dark parts of the picture and home-theater projectors that are much less bright but much better at showing shadow details. So even if you get something that is passable in a bright room, it will look like a cheap tv when it comes time to watch a movie at night.
Maybe you could figure out a way to hang an LCD tv such that it could "flip up" and lay flat against the ceiling when not in use. Or go with motorized black-out blinds for your windows, so you can make the room dark with the push of a button even when it is the middle of the day . That is the route I took to make a 120" screen work in my living room with 8 big picture windows.