Spent brewing grains can be composted. Like anything else put into be composted a number of things will determine what detectable odors you might find. If the spent grains are too wet when put in you will get an odor that some might consider objectionable while others won't. Since the spent brewing grains are used as animal feed they most likely have pretty good nutrient levels so your mix will need to be about the same as manure and vegetative waste shold be, 1 part spent brewery grains to 3 parts vegetative waste.

1 part spent brewery grains to 3 parts vegetative waste.

So are these grains considered as "browns"?

I was thinking of mixing sawdust with this material to minimize the odour given that I am in a "cheek to jowl" residential neighbourhood.

I have used it many times and from my first experience it can be quite "fragrant" if left in a pile.
I would mix it with shredded leaves ,paper, hay, straw and other high high carbon browns.
I've also tilled it into the soil.
I think it's a great source of free material ,just treat it with a little caution and don't let it rot on it's own. I agree with Kim on the 1:3 ratio but I would stay away from vegetative waste that tends to be a green and tends to be moist. With spent grains you want dry browns.
On the other hand if you hate your neighbors mix the spent grains with freshly mowed grass. Back in the days when I thought greens were green and browns were brown. ooooh boy things got pungeant. lol

rouge 21 they are definitely a green. Sawdust would be perfect.

It's decent, not great, nitrogen (green) feed. It can become aromatic. As received from the mashing process they will be water saturated. You will want to use a good, dry brown material with high bulk.

A link below from the University of Alaska Coop Extension Service on the subject.

Here is a link that might be useful: Using Spent Brewery Grain in the Alaska Compost Pile

I have a mostly raised garden bed that I created last fall. And so the earth, once it thaws out, will be quite loose i.e. not compact. Given that these grains are considered "greens", would it be beneficial to till or even hand dig these spent grains into this earth (knowing that I intend to plant perennials this spring)?

Yes, I would bury them, otherwise half the N will go up in the air. The nutrient profile is similar to chicken manure (high N, medium P, moderate K). For garden maintenance (where, due to repeated composting, you have high nutrient levels) it would be ideal.

Thanks glib. And so unlike having too fresh manure I could plant right away in this garden with the grains dug in below?