You can visit almost any big box store to see that most dishwashers can freestand on their own, on their 4 feet, so as long as the board is long enough front-to-back, I wouldn't see a problem with it fitting.

The biggest concern I would worry about is securing it somehow to prevent it from tipping forward when the door is down and the racks are rolled out and loaded with heavy dishes. Normally this is just covered by the countertop, but other appliances (like our oven/stove) will use hook & notches secured into the back wall to avoid the tipping risk.

Even more so of a concern since your dishwasher will be elevated a bit, so a forward tumble could be way way worse.