In short, yes, but how much would depend on how long it is held and how it is handled. Simply the act of removing the protective skin opens the clove to air and deterioration, but not enough I would be concerned if the cloves are used in a reasonable period, the sooner the better.
Now, the shaking in a pot will tend to bruise the cloves. In doing so, you are rupturing cell membranes and increasing the deterioration speed. Slicing, crushing, mincing, etc., you have just multiplied that effect. The more you break down the cloves, the faster it is going to degrade on you.
Think in part this way, if you can smell garlic, or see the oils, you are losing some of its essence right there, and you are exposing it to air which is increasing any bacterial or chemical reactions. I would stop at the point of peeling and retain whole cloves, not process further than that until read to use myself.
Also note, some people, if they are going to use oil with the garlic anyway, will go ahead and mince, chop, or slice and drop into olive oil. Be cautious with this! It will trap you garlic goodness in the oil, but it will also create an air tight low acid environment which is a danger zone.