Horizontal Drains Can Combine Through Wye Laying Flat, Or Can't They?
Yes, it is/has been done often. If you can, I personally prefer to put the wye so that the offshoot is angled slightly down into the main run to create a natural direction for flow.

The only thing I'd caution you on, if your code is picky about it, calculate your DFUs to make sure it is acceptable.

Also... I was looking at your drawing, and this is 100% my personal preference only, I dislike taking the first floor vent off of the second floor flow. If possible I would tap the line ABOVE where the second floor fixtures enter the stack and run that as a second line down to the first floor vents. As far as I know there's no code that requires it, but I prefer to keep my vents dry at all times. (Which you have done in the drawing)