Do it - you will appreciate it. One of the first things that drove me nutz after I quit was the lingering odor in my coat, my man purse, my hats... It's not like you can get away from the odor if you are wearing it. I couldn't wait to run that stuff through a good washing. Other things could wait on getting cleaned up, but those used every day items had to get cleaned ASAP.
We have over 100 shirts that are hanging in the closet that have a slight stench to them. The sheer number we have is why I'm not washing them. I'll just have to deal with the linger.