J, it should work fine for birds if you are not taking long shots (over 30 yards??).
Best way to know for sure is to buy some butcher paper or newsprint and pattern the gun with some different loads. That is, shoot different loads at a paper target at different distances and see what the patterns look like. Its traditional to draw a 30" circle on the paper and count the pellets, but that's too much work for me. I draw circles and just look at what the pattern looks like relative to my point of aim.
My brother got a Winchester 1300 defender with 18" barrel (20"?) and when we patterned it, we saw good patterns with size 6 shot out to about 25-30 yards. He let my son take it hunting once, but we didn't get any shots...
Any way, see how it shoots with different loads and you'll find what your effective range is.
By the way, my brother got a quote for putting screw-in choke tubes on his Win. It was $40 for the "drilling" and then $25 or so per choke tube. A tighter choke (like modified or full) would give you better range for those grouse. Something to consider...