I wouldn't. Downsizing isn't really meant to be a beginner thing, it's really not beginner friendly. The whole point of downsizing is to have better control and performance for the more difficult and advanced routes, beginners don't climb on advance routes that require high performance shoes or downsizing.
I would hold off on downsizing and only do it when you get to the higher grades and are more knowledgeable in climbing and climbing shoes, it's a whole world out there!
I have taken a few breaks from climbing here and there, sometimes for a few months at a time, and each time my shoes felt more like plastic than I remembered. It's not to the point where it's a whole new break-in process, but, it usually takes about a session or two to get used to them again. It's really about getting my feet used to climbing shoes again, the shoes usually keep the shape they had before I took my break, it's my feet that need to re-adapt to the tightness of the shoes.
I have washed my chalk bag a few times throughout the years, not that it was REALLY needed, but, I personally like to refresh my gear after sometime. Other gear I might buy new, but chalk bags I feel can just live on until they are really in bad shape and ruined, especially because they are not a matter of safety. When it comes to safety or performance, like quick draws or shoes, I would buy new, but chalk bags don't fit those categories so I just keep them for as long as they last and give them a little wash if I want to "renew" them.
