Just how much and how quickly the aluminium gets back in the sky depends on a few things.
Fairly large parts from aircraft which have very distinct alloy usages in distinct parts of the airframe are easily sorted at the break down stage so these can be meletd & recycled into a new batch of their given alloy as soon as there is a melt of that grade.
What helps is this instance as well is that most parts are designed to have a serial number always visible on them, which makes tracing the alloy grade dead easy. What doesn't help is when the tear down splits parts into two or more pieces.
When the parts aren't easily identified as any given alloy, then it's into the general melt. If the foundry is a specialist producer of aviation grade alloys, then they'll melt a batch of material to see which grade the resulting mix is closest to and then add either more scrap where the grade is known, or they'll add relatively pure ingredients into the melt to bring the overall balance of chemical elements into the ranges for each one within the alloy grade, or to bring the alloy mix into the range for a specific grade if they have an oder for that grade.
If they don't have a specific need then they'll often melt the scrap into batches and take an analysis of each one before casting it into ingots. In that way they can put material into stock, knowing then just what they need to add into the mix to take each "stock-melt" into a given alloy.
This doesn't just happen with aluminium, or aluminum to our US colleagues, but with the vast majority of metals currently in service. Sometimes of course, it actually takes an addition of a compound maybe limestone and maybe oxygen blown through to remove undesirable elements from a melted alloy to meet the specified limits.
Metal recycling is nothing new - I recall from my college days our metallurgy lecturer telling us that most modern steel has been recycled between 5 and 10 times and that aluminium was fast catching up, despite the increasing exploitation of reserves and increasing volume of these materials being produced annually.
Hope this helps.