Where are you located?
A lot of people recommend waiting to plant in a hugelbed until it's settled for a while. I'm miserly (maybe frugal is a better word?) and I couldn't bear to waste the time, materials, and space by not planting into it right away. They did fantastically well. I feel like planting into it actually helped the bed to settle down in a way, and because I had plants in it, I was better about watering and keeping it mulched through the season.
I don't know what the optimal amount of precipitation is for them. My hugelbeds help control and drain excess water, which is a plus.
I wouldn't bother waiting for the logs to be that weathered, because depending on their current condition, that won't be for a long time, and the bed should grow fine in the meantime. I mulch with rabbit bedding at the beginning and middle of the season, and with grass clippings, weeds, etc all the time. When I feel like it/remember to I add
compost teas of various kinds. I keep an eye on the plants to watch for nitrogen shortages but haven't noticed any problems.