The conditions will be different from year to year, but I did the Coleman-Demming as one of my first glacier routes in May of 2006 and can comment on my experiences.
I thought it was a great beginning glacier travel route. It's not very steep so it allowed us to concentrate more on our glacier travel technique. We did it in three days - one day up to camp, one day to practice crevasse rescue, and a day to summit and come all the way back down and out. All of the crevasses were covered while we were there, but you could just barely detect quite a few. I led the climb and punched through twice.
Some PNW veterans can probably comment more on possible conditions, but the weather will be a crapshoot in May. We got snowed on on our 2nd day, and rain the morning of our summit day, but we climbed through it and had a great summit day. Got lucky I think.
As far as avalanche safety, best to watch and check current conditions over the final few weeks before your trip, IMO. I remember the rangers up there being very helpful and knowledable about current conditions. Obviously if it dumps several feet of snow the week before your trip, you'll want to reconsider. We carried beacons/probes/shovels.
If your schedule is flexible, go when conditions and weather are best. We flew up there and didn't have that luxury.
Still one of my favorite climbs of all time, such a beautiful mountain. We had an amazing campsite overlooking the Roosevelt Glacier, and watched huge pieces of ice falling down the upper Roosevelt.
I say make sure you know your glacier travel /crevasse rescue/self arrest and go for it!