In theory, yeah. It reacts to super tiny movements of your head so you will get that constant micro parallax effect. I could cover one eye in VR and my depth perception would be kinda bad, but not gone. A lot of the effect is that the lenses let your eye focus out 10-20-30 feet even though the display is right there. There's actually a lot going on to create the effect that has nothing to do with binocular vision or even good vision in general. I'm sure there are cases were it wouldn't work right, but it's probly worth a shot.
It will work. The feeling of presence is not lost without stereoscopy - just like in real life. The main appeal of VR is 1:1 scale, and ultra-precise all-axis headtracking (which will sort of mend the lack of stereoscopy for you) .
That's exactly why I think it's a disservice to avoid the VR. Everything is tailored to VR and the controllers. It takes time to reload! You have to eject the magazine and insert a new one. You get surrounded & flanked by enemies and your movement speed, head-turning are dictated by your real world physical state. You have to physically duck and move and take cover in Alyx. When you are in a dark corridor and you hear enemies but cannot see them yet, it is a whole other level of experience to the same scenario on a flat screen with a mouse & keyboard. You have to use a flashlight in one hand and your gun in the other while looking all over to make sure your back is not exposed to enemy attack. It gets intense at parts. And of course, being developed by Valve, the whole package is the highest level of quality.