For individual sales, maaaaaaaybe. For company sales, not a chance. Any large company will most likely have agreements with one of the Big 3 and exclusively buys from them across the company. Big companies aren't going to try to play around and see if Asus or Acer can give them the support that the Big 3 do.
The biggest issue I see is that for the longest time they've shipped systems with terrible displays (72% sRGB gamut anyone?), and regardless of how powerful the GPU was/is, that's useless for serious color work. This will come back to bite them in the a** if they don't offer better displays across the workstation range (down to the Precision 3000 series and equivalent budget machines by HP/Lenovo)
I'm assuming this is partially why Lenovo upgraded the display choices on the X1 Extreme Gen 2 (and will likely carry over to the P1 Gen 2), as they now include Pantone X-Rite calibration, 100% Adobe gamut coverage, etc, and there are more choices than the 1st gen (1st gen was limited to FHD 90ish% sRGB , or 4K 100% sRGB Touch).