If you are hunting grouse and you've got a shotgun in your hands, you are obligated as a fair chase hunter to shoot them on the wing. And a .410 in inexperienced hands is just going to be frustrating. Especially a single shot.
You have some options. Head to the skeet range or a gravel pit next summer, and spend a lot of time and money getting good with the most difficult 'gauge' shotgun to shoot. Lessons will be mandatory. Another option is to find a cheap, used, s/s 20 gauge gun and see that it gets a very open choke. You will be able to hit targets easier and learn wingshooting faster this way, so the money you save on .410 shells will buy you that 20 gauge gun.
But by all means go out and hunt! You will very soon see that shooting grouse on the ground is no challenge. The excitement and love of grouse hunting begins with the flush. When they burst out of nowhere with wings thundering, your heart stops and your eyes dart everywhere trying to find a streaking brown bomb through the branches. If you can see it you can try to get off a shot, but more often than not you'll miss! On with the chase, as you head off in the direction the bird went, your heart pounding, hopefully to get another flush and a shot. I'll take 10 flushes and 10 misses over a single shot at a bird on the ground any day.
But take warning; once you're hooked, you're hooked.
Grouse Man