Nope.
You could on the other hand produce a LUT in photoshop that would approach the result you wanna get.
If you're using a B&W LUT, putting another LUT on top would make it different. LUT is shifting the channels hue. So putting let's say, a LUT that does a big shift in the green and blue and only keeps the red, would appear far different after putting a B&W first.
You wouldn't get the result "you think" you're gonna get by slapping them together.