To my knowledge, aeration provides oxygen so that the yeast can reproduce before fermentation. If you're pitching onto an existing yeast cake, there should theoretically be enough yeast already to begin fermentation without needing to reproduce.
Should the wort be aerated anyway (or should it not be)? Does the particular beer make a difference (i.e. pitching the same recipe as before vs. pitching a different recipe)?
In short, depending on the age of the cake there should be no need to re-aerate the wort for growth purposes. Using the full on yeast cake will make fine beer without the need of extra O2 for yeast growth.
The downside to this practice is that without some active reproduction going on you don't always get the true flavor profile of the yeast in the beer. I have pitched the same English Pale recipe directly on the cake from the last run of a beer in order to make twice that amount of beer (and save on yeast). But the resulting beer had very little of the English yeast character that the first batch had. The second batch tasted more clean, much like WLP001 American Ale yeast.
The best practice when using cake is to harvest some of the cake and repitch it into well aerated wort. The benefit of using cake this way is that you do not need to do a starter to get the proper cell count for pitching. But you do need to aerate inorder to have that pitch growth enough for proper flavor development.
If you're concerned about using good practice, you really shouldn't rack fresh wort onto a used yeast cake. The trub contains a lot more than just healthy yeast, and doing this doesn't allow you to control your pitch rate. I know that doesn't really answer the question, but it seems that your general procedure leaves more room for error than the oxygen factor.
EDIT: Downvote all you want, but I quote:
A number of homebrewers have adopted the practice of transferring the beer from a fermentor and the end of fermentation and then adding a new batch of wort on top of the yeast cake. This is a bad practice. Can this practice make good beer? Absolutely. Will it make the best beer possible? Absolutely not. The yeast at the end of fermentation is not just healthy yeast. There are plenty of dead cells present, as well as the break material and hop bits from the previous wort. You must collect the yeast, look at the population, remove dead cells and nonyeast material by rinsing, and then reuse only the proper quantity of cells in the next batch. Do not be lazy. Always clean and sanitize your fermentor between batches, and always ensure you are pitching the correct number for cells for the beer you are brewing. Yeast growth is important to beer flavor, and overpitching (especially with excessive trub) can have a negative effect.
Source: White, C. and Zainasheff, J. Yeast: The Practical Guide to Beer Fermentation. p 164.
So yes, reusing yeast is fine, but racking fresh wort onto old yeast is not fine. Not that you can't do it, just that it's sloppy. If you're gonna do it, though, might as well not bother with aeration.
I don't have definitive evidence one way or another, but here's my thoughts on the matter.
The two or three times I have pitched onto an existing yeast cake, I have always followed my standard aeration procedure and things have been fine. Good fermentation, etc.
My thought is this: If you are going to pitch on an existing yeast cake (setting arguments about whether this is good practice or not aside), aerate like normal. Aeration is part of the normal process and if nothing else, practice makes perfect.
On top of that, considering there might be side-effects of NOT aerating, why not do it?
Probably not the best answer to your question, but that's where I stand on it.
You should not need to aerate. The purpose of the aerobic stage of the yeast lifecycle is reproduction and if you are pitching on a an existing yeast cake, there should be no need to build up your yeast count.
It depends on the two recipes. If you are pitching a beer with a higher OG than the batch that the yeast cake was formed by, I think that aeration would be more important than if you were going from a higher OG to a Lower one.
